Search NASA⌕ Search

SEARCH · Search NASA

Results for “Fractional derivative”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 91 records · Page 5

Effects of 9.5 Years of Whole-Soil Warming on the Fatty Acid and n-Alkanes Composition in Bulk Soil and Density Fractions at Blodgett Experimental Forest, California, USA

Original data of molecular data (fatty acids and n-alkanes) including concentrations and calculated molecular proxies in a whole-soil warming experiment at the Blodgett Forest Research Station after 9.5 years of warming. The study site has a Mediterranean climate with annual average temperature of 12.5 ℃ and annual average precipitation of 1774 mm. The study site is characterized by a mesic Ultic Alfisol formed from granitic parent material, corresponding to a Dystric Cambisol under the World Reference Base for Soil Resources (WRB) classification system. Experimental warming is applied throughout the soil profile to a depth of 1 m using vertically embedded heating cables that raise soil temperature by 4 °C relative to ambient conditions. Soil samples were collected on 1 May 2023, after the experiment had been operating continuously for about 9.5 years since its initiation in January 2014.The data has been processed from raw data and cross-validated by other peers. The dataset includes: - Bulk_Fattyacid_9.5-year_Soil_Warming_Blodgett, California, USA: fatty acid concentrations and proxies including Carbon Preference Index (CPI) and Average Chain Length (ACL) of bulk soil organic carbon; - Fractions_Fattyacid_9.5-year_Soil_Warming_Blodgett, California, USA: fatty acid concentrations and proxies including CPI and ACL of free particulate organic matter (fPOM) and mineral-associated organic matter (MAOM); - Bulk_Alkanes_9.5-year_Soil_Warming_Blodgett, California, USA: n-alkanes concentrations and proxies including CPI and ACL of bulk soil organic carbon; - Fractions_Alkanes_9.5-year_Soil_Warming_Blodgett, California, USA: n-alkanes concentrations and proxies including CPI and ACL of fPOM and MAOM; - n-Alkanes_All_Monomer_Concentration_9.5-year_Soil_Warming_Blodgett, California, USA: concentration of all the n-alkane monomers identified and integrated for bulk soil, fPOM and MAOM; - Fattyacid_All_Monomer_Concentration_9.5-year_Soil_Warming_Blodgett, California, USA: concentration of all the fatty acid monomers including diacids identified and integrated for bulk soil, fPOM, and MAOM. All data are provided in CSV format and can be viewed using Microsoft Excel. We specifically look at fatty acids (FA) and n-alkanes in bulk soil, fPOM and MAOM and calculated molecular proxies such as CPI and ACL to understand the source of oragnic carbon (with ACL) and degree of decomposition (CPI) of each soil fraction. Due to lack of long-chain fatty acids (carbon number ⩾ 20), microorganism-derived organic carbon is characterized by shorter ACL in comparison to plant-derived organic carbon. Fresh SOC is characterized by even-over-odd dominance for fatty acids and odd-over-even dominance for n-alkanes. Therefore, CPI indicates whether soil organic carbon (SOC) represents fresh input (CPI > 10) or is strongly decomposed (close to 1). The research questions should be then, after 9.5-year warming: 1. whether the relative contribution between microorganism-derived and plant-derived SOC in each soil fraction? 2. whether fPOM became more decomposed whereas MAOM remained relatively persistent in each soil fraction across the soil depth?

Carbon↗

Cu‐Catalyzed Aerobic Oxidative C─C Cleavage in Lignin‐Derived Oligomers and Biological Funneling of the Monomeric Products

Existing methods for lignin deconstruction to aromatic monomers primarily cleave carbon–oxygen bonds within the polymer, resulting in sub-optimal monomer yields and formation of oligomers that retain intact carbon–carbon bonds. Here, we demonstrate that copper-catalyzed aerobic oxidation under aqueous alkaline conditions promotes oxidative cleavage of carbon–carbon bonds in lignin oligomers derived from reductive catalytic fractionation (RCF) of pine and poplar biomass. Fundamental insights are gained from reactions of model compounds that resemble subunits present in RCF oligomers. Optimal results are achieved in a flow reactor that provides precise control over O2 delivery, temperature, and reaction residence time. The Cu-catalyzed aerobic oxidation conditions access aromatic monomers in 19 and 34 wt% monomer yields, respectively, from pine- and poplar-derived RCF oligomers. Overall, the sequence consisting of biomass RCF into monomers and oligomers followed by oxidative deconstruction of the RCF oligomers generates substantially higher yields of aromatic monomers from lignin. Engineered strains of Pseudomonas putida support biological funneling of the oligomer-derived oxygenated aromatic compounds into cis,cis-muconic acid from pine or 2-pyrone-4,6-dicarboxylic acid from poplar.

09 BIOMASS FUELS↗

Lignin-Derived Phenolic Compounds and Water Are Effective Cosolvents for Reductive Catalytic Fractionation

Reductive catalytic fractionation (RCF) is an effective lignin-first biorefining method to extract lignin as a stabilized oil from lignocellulosic biomass. To realize RCF at scale, process modeling has shown that minimizing the use of exogenous organic solvents is critical. To this end, here we investigate the ability of lignin-derived monomers to act as either solvents or cosolvents for RCF. We begin by examining the influence of lignin-derived aromatic compounds (4-propylguaiacol, 4-propylphenol, and propylbenzene) on RCF monomer yields and subsequently extend our analysis to mixtures of 4-propylguaiacol and either methanol or water. We demonstrate that 4-propylguaiacol is an effective solvent for lignin extraction and depolymerization during RCF, especially when used in combination with water as a cosolvent. Cosolvent mixtures of 4-propylguaiacol and water enable up to 81% lignin extraction, monomer yields up to 25 wt %, and postreaction phase separation. However, unlike methanol, water as a cosolvent fails to inhibit aromatic ring hydrogenation when conducted over Ru/C as a catalyst, potentially leading to excess hydrogen consumption in a process utilizing this approach. Nonetheless, these results suggest a promising strategy for eliminating external organic solvents from RCF by utilizing mixtures of lignin-derived compounds and water as alternative extraction solvents.

biorefining↗

Tabulated data for Lignin-Derived Phenolic Compounds and Water Are Effective Cosolvents for Reductive Catalytic Fractionation

Reductive catalytic fractionation (RCF) is an effective lignin-first biorefining method to extract lignin as a stabilized oil from lignocellulosic biomass. To realize RCF at scale, process modeling has shown that minimizing the use of exogenous organic solvents is critical. To this end, here we investigate the ability of lignin-derived monomers to act as either solvents or cosolvents for RCF. We begin by examining the influence of lignin-derived aromatic compounds (4-propylguaiacol, 4-propylphenol, and propylbenzene) on RCF monomer yields and subsequently extend our analysis to mixtures of 4-propylguaiacol and either methanol or water. We demonstrate that 4-propylguaiacol is an effective solvent for lignin extraction and depolymerization during RCF, especially when used in combination with water as a cosolvent. Cosolvent mixtures of 4-propylguaiacol and water enable up to 81% lignin extraction, monomer yields up to 25 wt %, and postreaction phase separation. However, unlike methanol, water as a cosolvent fails to inhibit aromatic ring hydrogenation when conducted over Ru/C as a catalyst, potentially leading to excess hydrogen consumption in a process utilizing this approach. Nonetheless, these results suggest a promising strategy for eliminating external organic solvents from RCF by utilizing mixtures of lignin-derived compounds and water as alternative extraction solvents. This is the tabulated data for the paper

biorefining↗

Search for the decay of the Higgs boson to a pair of light pseudoscalar bosons in the final state with four bottom quarks in proton-proton collisions at $ \sqrt{\textrm{s}} $ = 13 TeV

A search is presented for the decay of the 125 GeV Higgs boson (H) to a pair of new light pseudoscalar bosons (a), followed by the prompt decay of each a boson to a bottom quark-antiquark pair, $ \textrm{H}\to \textrm{aa}\to \textrm{b}\overline{\textrm{b}}\textrm{b}\overline{\textrm{b}} $. The analysis is performed using a data sample of proton-proton collisions collected with the CMS detector at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb$^{−1}$. To reduce the background from standard model processes, the search requires the Higgs boson to be produced in association with a leptonically decaying W or Z boson. The analysis probes the production of new light bosons in a 15 < m$_{a}$ < 60 GeV mass range. Assuming the standard model predictions for the Higgs boson production cross sections for pp → WH and ZH, model independent upper limits at 95% confidence level are derived for the branching fraction $ \mathcal{B}\left(\textrm{H}\to \textrm{aa}\to \textrm{b}\overline{\textrm{b}}\textrm{b}\overline{\textrm{b}}\right) $. The combined WH and ZH observed upper limit on the branching fraction ranges from 1.10 for m$_{a}$ = 20 GeV to 0.36 for m$_{a}$ = 60 GeV, complementing other measurements in the μμττ, ττττ and bbℓℓ (ℓ = μ, τ) channels.[graphic not available: see fulltext]

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Search for a new scalar resonance in flavour-changing neutral-current top-quark decays $t → qX (q = u, c)$, with $X → b\overline{b} $, in proton-proton collisions at $ \sqrt{s} $ = 13 TeV with the ATLAS detector

A search for flavour-changing neutral-current decays of a top quark into an up-type quark (either up or charm) and a light scalar particle X decaying into a bottom anti-bottom quark pair is presented. The search focuses on top-quark pair production where one top quark decays to qX, with X → $b\bar{b}$, and the other top quark decays according to the Standard Model, with the W boson decaying leptonically. The final state is thus characterised by an isolated electron or muon and at least four jets. Events are categorised according to the multiplicity of jets and jets tagged as originating from b-quarks, and a neural network is used to discriminate between signal and background processes. The data analysed correspond to 139 fb –1 of proton–proton collisions at a centre-of-mass energy of 13 TeV, recorded with the ATLAS detector at the LHC. The 95% confidence-level upper limits between 0.019% and 0.062% are derived for the branching fraction $\mathcal{B}$(t → uX) and between 0.018% and 0.078% for the branching fraction $\mathcal{B}$(t → cX), for masses of the scalar particle X between 20 and 160 GeV.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Understanding the influence of solvents on the Pt-catalyzed hydrodeoxygenation of guaiacol

Bio-oil derived from fast pyrolysis of lignocellulosic biomass needs to be deoxygenated to become a substitute for petroleum fuels. Here, we study the hydrodeoxygenation mechanism of guaiacol, a bio-oil model compound derived from the lignin fraction of biomass, on Pt(1 1 1) terrace sites in the presence of water, diethyl ether, 1-butanol, and n-hexane as solvent. Using first-principles periodic density functional theory (DFT) calculations and mean-field microkinetic reactor modeling, a detailed reaction mechanism is investigated targeting various products such as catechol, phenol, anisole, benzene, cyclohexanone, and cyclohexanol. Solvent phase DFT outcomes are mostly similar to that of the vapor phase; however, microkinetic modeling results suggest that rate controlling species and transition states differ somewhat in the various reaction environments. Catechol was found to be the major aromatic product across all reaction environments. Over Pt(1 1 1), unsaturated monooxygenate production from catechol is unlikely.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Tuning Solid Electrolyte Interphase Formation before Plating Onset in Anode-Free Sodium Batteries

Sodium (Na) batteries are of growing interest due to the higher earth abundance of sodium than lithium, as well as their promising theoretical energy density when metallic Na anodes are used. However, Na plating and stripping are heavily influenced by the physicochemical properties of the solid electrolyte interphase (SEI), which is directly influenced by the solvent and salt used for the electrolyte. While most studies focus on the SEI that forms on the surface of Na metal after plating, we expand this analysis by identifying a nanoscale “pre-plating” SEI that forms on the current collector (CC) prior to the onset of Na plating. Here, we systematically investigate an array of Na salt and glyme solvents in the electrolyte and determine the associated impacts on pre-plating SEI formation on aluminum CCs. By combining analytical electrochemistry approaches with a multimodal suite of spectroscopy techniques (X-ray, infrared, and Raman), supported by density functional theory calculations, we reveal a direct correlation between the Na + coordination environment and pre-plating SEI composition. We find that longer-chain glymes produce larger proportions of organic alkoxide products in the interphase, consistent with increased Na + −glyme interactions, while the fraction of salt-derived inorganic products (e.g., NaF) correlates with Na + −anion coordination. These insights highlight the critical influence of electrolyte composition particularly solvent identity and Na + coordination on the initial SEI formation in anode-free Na batteries.

anode-free batteries↗

Quantifying the Diversity of an Atmospheric Aerosol Population in an Arctic Oil Field on a Single‐Particle Level

As the Arctic rapidly warms, sea ice extent is decreasing and oil and gas extraction activities are expanding. Local combustion emissions affect the Arctic atmospheric aerosol chemical mixing state (the distribution of chemical species across the aerosol population), which impacts climate-relevant properties. Bulk and single-particle measurements of submicron aerosols were conducted at Oliktok Point, Alaska within the North Slope of Alaska oil fields. In this work, we quantify aerosol diversity using online single-particle mass spectrometry data (32,880 individual particles), offline single-particle microscopy data (20,912 individual particles), and online bulk aerosol mass spectrometry and aethalometer data. This method was used to derive individual particle mass fractions for both refractory and non-refractory material within distinct particle types. Single-particle, average single-particle, and bulk population diversities (D i , D α , D γ , respectively) and mixing state indices (χ) were calculated for the data set. Calculated D i values were generally low (2.2 ± 0.6), as individual particle masses were dominated by a few chemical species of interest. Aged aerosol particles (those internally mixed with nitrate and/or sulfate) exhibited higher D i values (>3) compared to recently emitted (fresh) aerosol particles. During oil field plume periods, D α values approached three due to the abundance of diesel combustion particles, which were rich in sulfate, black carbon, and organic aerosol. Overall, the submicron aerosol population within the Arctic oil fields was found to be relatively externally mixed (χ < 50%), due to the constant local emissions within oil fields combining with background aerosol and locally emitted sea spray aerosol at the coastal site.

Wu, J.↗

Constraints on compact objects from the Dark Energy Survey 5-yr supernova sample

ABSTRACT Gravitational lensing magnification of Type Ia supernovae (SNe Ia) allows information to be obtained about the distribution of matter on small scales. In this paper, we derive limits on the fraction $\alpha$ of the total matter density in compact objects (which comprise stars, stellar remnants, small stellar groupings, and primordial black holes) of mass M > 0.03 ${\rm M}_{\odot }$ over cosmological distances. Using 1532 SNe Ia from the Dark Energy Survey Year 5 sample (DES-SN5YR) combined with a Bayesian prior for the absolute magnitude M, we obtain α < 0.12 at the 95 per cent confidence level after marginalization over cosmological parameters, lensing due to large-scale structure, and intrinsic non-Gaussianity. Similar results are obtained using priors from the cosmic microwave background, baryon acoustic oscillations, and galaxy weak lensing, indicating our results do not depend on the background cosmology. We argue our constraints are likely to be conservative (in the sense of the values we quote being higher than the truth), but discuss scenarios in which they could be weakened by systematics of the order of $\Delta \alpha \sim 0.04$.

79 ASTRONOMY AND ASTROPHYSICS↗

CO2 refixation is higher in leaves of woody species with high mesophyll and stomatal resistances to CO2 diffusion

Abstract The percentage of respiratory and photorespiratory CO2 refixed in leaves (Pr) represents part of the CO2 used in photosynthesis. The importance of Pr as well as differences between species and functional types are still not well investigated. In this study, we examine how Pr differs between six temperate and boreal woody species: Betula pendula, Quercus robur, Larix decidua, Pinus sylvestris, Picea abies and Vaccinium vitis-idaea. The study covers early and late successional species, deciduous broadleaves, deciduous conifers, evergreen conifers and evergreen broadleaves. We investigated whether some species or functional types had higher refixation percentages than others, whether leaf traits could predict higher Pr and whether these traits and their impact on Pr changed during growing seasons. Photosynthesis CO2 response (A/Ci)-curves, measured early, mid and late season, were used to estimate and compare Pr, mesophyll resistance (rm) and stomatal resistance (rs) to CO2 diffusion. Additionally, light images and transmission electron microscope images were used to approximate the fraction of intercellular airspace and cell wall thickness. We found that evergreens, especially late successional species, refixed a significantly higher amount of CO2 than the other species throughout the entire growing season. In addition, rm, rs and leaf mass per area, traits that typically are higher in evergreen species, were also significantly, positively correlated with Pr. We suggest that this is due to higher rm decreasing diffusion of (photo) respiratory CO2 out of the leaf. Cell wall thickness had a positive effect on Pr and rm, while the fraction of intercellular airspace had no effect. Both were significantly different between evergreen conifers and other types. Our findings suggest that species with a higher rm use a greater fraction of mitochondria-derived CO2, especially when stomatal conductance is low. This should be taken into account when modeling the overall CO2 fertilization effect for terrestrial ecosystems dominated by high rm species.

59 BASIC BIOLOGICAL SCIENCES↗

Toward a Ginsparg-Wilson lattice Hamiltonian

To address quantum computation of quantities in quantum chromodynamics (QCD) for which chiral symmetry is important, it would be useful to have the Hamiltonian for a fermion satisfying the Ginsparg-Wilson (GW) equation. I work with a solution to the GW equation which is fractional linear in time derivatives. The resulting Hamiltonian is nonlocal and has ghosts, but is free of doublers and has the correct continuum limit. This construction works in general odd spatial dimensions, and I provide an explicit expression for the Hamiltonian in one spatial dimension. Published by the American Physical Society 2024

Astronomy & Astrophysics↗

Lignin-Derived Phenolic Compounds and Water Are Effective Cosolvents for Reductive Catalytic Fractionation

Reductive catalytic fractionation (RCF) is an effective lignin-first biorefining method to extract lignin as a stabilized oil from lignocellulosic biomass. To realize RCF at scale, process modeling has shown that minimizing the use of exogenous organic solvents is critical. To this end, here we investigate the ability of lignin-derived monomers to act as either solvents or cosolvents for RCF. We begin by examining the influence of lignin-derived aromatic compounds (4-propylguaiacol, 4-propylphenol, and propylbenzene) on RCF monomer yields and subsequently extend our analysis to mixtures of 4-propylguaiacol and either methanol or water. Here, we demonstrate that 4-propylguaiacol is an effective solvent for lignin extraction and depolymerization during RCF, especially when used in combination with water as a cosolvent. Cosolvent mixtures of 4-propylguaiacol and water enable up to 81% lignin extraction, monomer yields up to 25 wt %, and postreaction phase separation. However, unlike methanol, water as a cosolvent fails to inhibit aromatic ring hydrogenation when conducted over Ru/C as a catalyst, potentially leading to excess hydrogen consumption in a process utilizing this approach. Nonetheless, these results suggest a promising strategy for eliminating external organic solvents from RCF by utilizing mixtures of lignin-derived compounds and water as alternative extraction solvents.

09 BIOMASS FUELS↗

Phase-field modeling of solid-state metathesis reactions with the charge neutrality constraint

In this work, we present a phase-field model that captures the evolution of ionic concentrations and phase fractions during solid-state metathesis (SSM) reactions where diffusion limits the rate of transformation. The evolution of the mole fraction of each ion is obtained via governing equations that describe the reduction of a free energy, which includes an energy landscape with local minima located at compositions corresponding to stable products. We utilized two Lagrange multipliers to impose constraints of electroneutrality as well as on the sum of mole fractions, which were then eliminated to derive set of two partial differential equations that describe the dynamics of the mole fraction evolution. From these governing equations, the expressions for effective mobilities for the cations and the anions were obtained. We first study the effect of mobilities of ions on the reaction kinetics, using a simple model considering the ions with an identical absolute value of charge numbers. The simulation results show that the overall characteristic mobility, defined as the sum of the two effective ionic mobilities, provides an excellent measure of the rate at which reaction progresses and that the ratio of the effective mobilities of the anions and the cations signifies the manner by which the reaction progresses. We then generalize the model to consider ions with different charge numbers and tuned the mobility of ions based on their diffusion coefficients reported in the literature and experimental data from a thin-film experiment for the synthesis of FeS 2 to demonstrate the capability of the model to predict the phase evolution during SSM reactions. In particular, the simulation predicts nonplanar phase evolution, which is recently observed in thin-film reactions for the synthesis of FeS 2 via transmission electron microscopy. The approach can serve as a basis for models for phase transformations in other multiphase ionic mixtures, such as in all-solid-state batteries and in ionic liquids.

36 MATERIALS SCIENCE↗

Augmented reduced order models for turbulence

The authors introduce an augmented-basis method (ABM) to stabilize reduced-order models (ROMs) of turbulent incompressible flows. The method begins with standard basis functions derived from proper orthogonal decomposition (POD) of snapshot sets taken from a full-order model. These are then augmented with divergence-free projections of a subset of the nonlinear interaction terms that constitute a significant fraction of the time-derivative of the solution. The augmenting bases, which are rich in localized high wavenumber content, are better able to dissipate turbulent kinetic energy than the standard POD bases. Several examples illustrate that the ABM significantly out-performs L 2 -, H 1 - and Leray-stabilized POD ROM approaches. The ABM yields accuracy that is comparable to constraint-based stabilization approaches yet is suitable for parametric model-order reduction in which one uses the ROM to evaluate quantities of interests at parameter values that differ from those used to generate the full-order model snapshots. Several numerical experiments point to the importance of localized high wavenumber content in the generation of stable, accurate, and efficient ROMs for turbulent flows.

Kaneko, Kento↗

An optimization-based approach to parameter learning for fractional type nonlocal models

Nonlocal operators of fractional type are a popular modeling choice for applications that do not adhere to classical diffusive behavior; however, one major challenge in nonlocal simulations is the selection of model parameters. In this study we propose an optimization-based approach to parameter identification for fractional models with an optional truncation radius. We formulate the inference problem as an optimal control problem where the objective is to minimize the discrepancy between observed data and an approximate solution of the model, and the control variables are the fractional order and the truncation length. For the numerical solution of the minimization problem we propose a gradient-based approach, where we enhance the numerical performance by an approximation of the bilinear form of the state equation and its derivative with respect to the fractional order. Several numerical tests in one and two dimensions illustrate the theoretical results and show the robustness and applicability of our method.

97 MATHEMATICS AND COMPUTING↗

Intrinsic Ion Transport Properties of Block Copolymer Electrolytes

Knowledge of intrinsic properties is of central importance for materials design and assessing suitability for specific applications. Self-assembling block copolymer electrolytes (BCEs) are of great interest for applications in solid-state energy storage devices. A fundamental understanding of ion transport properties, however, is hindered by the difficulty in deconvoluting extrinsic factors, such as defects, from intrinsic factors, such as the presence of interfaces between the domains. Here, we quantify the intrinsic ion transport properties of a model BCE system consisting of poly(styrene-block-ethylene oxide) (SEO) and lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) salt using a generalizable strategy of depositing thin films on interdigitated electrodes and self-assembling fully connected parallel lamellar structures throughout the films. Comparison between conductivity in homopolymer poly(ethylene oxide) (PEO)-LiTFSI electrolytes and the analogous conducting material in SEO over a range of salt concentrations (r, molar ratio of lithium ion to ethylene oxide repeat units) and temperatures reveals that between 20% and 50% of the PEO in SEO is inactive. Using mean-field theory calculations of the domain structure and monomer concentration profiles at domain interfaces-both of which vary substantially with salt concentration-the fraction of inactive PEO in the SEO, as derived from conductivity measurements, can be quantitatively reconciled with the fraction of PEO that is mixed with greater than a few volume percent of polystyrene. Despite the detrimental interfacial effects for ion transport in BCEs, the intrinsic conductivity of the SEO studied here (ca. 10 -3 S/cm at 90 degrees C, r = 0.085) is an order of magnitude higher than reported values from bulk samples of similar molecular weight SEO (ca. 10 -4 S/cm at 90 degrees C, r = 0.085). Finally, this work provides motivation and methods for pursuing improved BCE chemical design, interfacial engineering, and processing.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

An optimization-based approach to parameter learning for fractional type nonlocal models

Nonlocal operators of fractional type are a popular modeling choice for applications that do not adhere to classical diffusive behavior; however, one major challenge in nonlocal simulations is the selection of model parameters. In this work we propose an optimization-based approach to parameter identification for fractional models with an optional truncation radius. We formulate the inference problem as an optimal control problem where the objective is to minimize the discrepancy between observed data and an approximate solution of the model, and the control variables are the fractional order and the truncation length. For the numerical solution of the minimization problem we propose a gradient-based approach, where we enhance the numerical performance by an approximation of the bilinear form of the state equation and its derivative with respect to the fractional order. Several numerical tests in one and two dimensions illustrate the theoretical results and show the robustness and applicability of our method.

97 MATHEMATICS AND COMPUTING↗