Numerical Solution of Fractional Differential Equations: A Survey and a Software Tutorial

By Roberto Garrappa. 2018

466 citations recorded by the source corpus.

Solving differential equations of fractional (i.e., non-integer) order in an accurate, reliable and efficient way is much more difficult than in the standard integer-order case; moreover, the majority of the computational tools do not provide built-in functions for this kind of problem. In this paper, we review two of the most effective families of numerical methods for fractional-order problems, and we discuss some of the major computational issues such as the efficient treatment of the persistent memory term and the solution of the nonlinear systems involved in implicit methods. We present therefore a set of MATLAB routines specifically devised for solving three families of fractional-order problems: fractional differential equations (FDEs) (also for the non-scalar case), multi-order systems (MOSs) of FDEs and multi-term FDEs (also for the non-scalar case); some examples are provided to illustrate the use of the routines.

Subfields: Control and Systems Engineering, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/c495271d02b6a02c1bd7772f2b5dbe0a0c4eecf6

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In Control and Systems Engineering

1. Mehmet Yavuz
2. Ndolane Sene

In Modeling and Simulation

1. Ndolane Sene
2. Mehmet Yavuz
3. Necati Özdemir

In Numerical Analysis

1. Ndolane Sene
2. Mehmet Yavuz
3. Necati Özdemir

Citations in the corpus

• Stability Analysis and Numerical Computation of the Fractional Predator–Prey Model with the Harvesting Rate (2020, background): “Substituting Equations (56) and (57) into Equations (54) and (55), respectively, the final numerical discretization of the P–PM in the context of the Caputo derivative is presented by the following form [73].”