swMATH ID: 44175
Software Authors: Moein Khalighi, Giulio Benedetti, Leo Lahti
Description: FdeSolver: A Julia Package for Solving Fractional Differential Equations. Implementing and executing numerical algorithms to solve fractional differential equations has been less straightforward than using their integer-order counterparts, posing challenges for practitioners who wish to incorporate fractional calculus in applied case studies. Hence, we created an open-source Julia package, FdeSolver, that provides numerical solutions for fractional-order differential equations based on product-integration rules, predictor-corrector algorithms, and the Newton-Raphson method. The package covers solutions for one-dimensional equations with orders of positive real numbers. For high-dimensional systems, the orders of positive real numbers are limited to less than (and equal to) one. Incommensurate derivatives are allowed and defined in the Caputo sense. Here, we summarize the implementation for a representative class of problems, provide comparisons with available alternatives in Julia and Matlab, describe our adherence to good practices in open research software development, and demonstrate the practical performance of the methods in two applications; we show how to simulate microbial community dynamics and model the spread of Covid-19 by fitting the order of derivatives based on epidemiological observations. Overall, these results highlight the efficiency, reliability, and practicality of the FdeSolver Julia package.
Homepage: https://arxiv.org/abs/2212.12550
Source Code:  https://github.com/JuliaTurkuDataScience/FdeSolver.jl
Dependencies: Julia
Keywords: Julia package; fractional differential equations; memory effects; numerical algorithms; predictor-corrector method; product-integration; Newton-Raphson method
Related Software: FractionalDiffEq.jl; Matlab; Optim; Turing; FOTF Toolbox; Pathogen.jl; Julia
Cited in: 0 Publications

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1 Publication describing the Software Year
FdeSolver: A Julia Package for Solving Fractional Differential Equationsia
Moein Khalighi, Giulio Benedetti, Leo Lahti