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version 1.0.0 (2.5 KB) by Roberto Garrappa
Solving nonlinear fractional delay differential equations (FDDEs) with one constant delay


Updated 11 Aug 2020

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Solves a nonlinear fractional delay differential equation (FDDE) with one constant delay tau > 0 in the form

D^alpha y(t) = g(t, y(t), y(t-tau))
y(t) = phi(t) t0-tau <= t <= t0

where D^alpha is the fractional Caputo derivative of order 0 < alpha < 1.

As initial data it must be provided not just a single value but a whole function phi(t) for t in the interval [t0-tau, t0].

The FDDE is solved by an explicit rectangular Product-Integration (PI) scheme suitably modified to solve FDEs with one constant delay.

Usage [t, y] = FDDE_PI1_Ex(alpha,g,tau,t0,T,phi,h)

Further information about this code are available in the Section 6 of the paper [1]; please, cite this code as [1].

Description of input parameters
alpha : fractional order of the delay differential equation; it must be 0 < alpha < 1
g : function handle evaluating the vector field g(t,y(t),y(t-tau))
tau : constant delay; it must be tau > 0
t0, T : starting and final time of the interval of integration
phi : function handle for the initial data phi(t)
h : integration step-size; it must be selected such that h <= tau

References and other information

[1] Garrappa R., Kaslik E.: On initial conditions for fractional delay differential equations, Communications in Nonlinear Science and Numerical Simulation, 2020, 90, 105359, doi: 10.1016/j.cnsns.2020.105359

Author: Roberto Garrappa (University of Bari, Italy)

Please, report any problem or comment to : roberto dot garrappa at uniba dot it

Cite As

Roberto Garrappa (2021). FDDE_PI1_Ex (, MATLAB Central File Exchange. Retrieved .

Comments and Ratings (2)

Bochra Ghani

How to use this function


Are there specific examples of applications,g and phi function is not well written.

MATLAB Release Compatibility
Created with R2020a
Compatible with any release
Platform Compatibility
Windows macOS Linux

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