The FDE-TestSet aims at collecting Matlab^® codes for solving initial value problems of fractional differential equations of Caputo type. The codes are compared in a systematic way on a set of test problems. For each problem, the used parameters for calling each code are listed. All tests have been performed on a 12-core M4-pro Silicon based computer with 64GB of shared memory, running Matlab^® 2024b.

We have considered the following Matlab^® codes (the description of each code is taken from Reference [1] below):

Hereafter, are the problems used for testing the codes (the description of each problem is taken from Reference [1] below), also reporting the obtained results, as here explained.

Problem description and WPD	Notes	Matlab® file	Codes compared
Problem 1	scalar problem, linear	prob1.m	all codes
Problem 2	scalar problem, linear	prob2.m	all codes
Problem 3	vector problem, linear	prob3.m	fde12, flmm2, fhbvm, fhbvm2
Problem 4	vector problem, linear, periodic solution	prob4.m	fde12, flmm2, fhbvm, fhbvm2
Problem 5	scalar problem, nonlinear	prob5.m	all codes
Problem 6	scalar problem, nonlinear	prob6.m	all codes
Problem 7	scalar problem, nonlinear	prob7.m	all codes
Problem 8	vector problem, nonlinear	prob8.m	fde12, flmm2, fhbvm, fhbvm2
Problem 9	vector problem, nonlinear, periodic solution	prob9.m	fde12, flmm2, fhbvm, fhbvm2
Problem 10	vector problem, nonlinear, periodic solution	prob10.m	fhbvm, fhbvm2
Auxiliary function for computing the Mittag-Leffler function for the solution of Problems 1-4	URL of the function license.txt	ml.m

We also provide the Matlab^®  files of the drivers used for the various codes:

Driver

driver_fde12.m

driver_flmm2.m

driver_fcoll.m

driver_tsfcoll.m

driver_fhbvm.m

driver_fhbvm2.m

mescd.m    (auxiliary function)

Reference:

[1] L.Brugnano, G.Gurioli, F.Iavernaro, M.Vikerpuur. FDE-testset: comparing Matlab^® codes for solving fractional differential equations of Caputo type. Fractal Fract. 2025, 9(5), 312; https://doi.org/10.3390/fractalfract9050312