MT_FDE_PI1_Im Solves on the interval [t0,T] an initial value problem for the multiterm fractional differential equation
lam_Q D^(al_Q) y(t) + ... + lam_1 D^(al_1) y(t) = f(t,y(t))
y(0) = y0(1), y'(0) = y0(2), ... y^m(0) = y0(m)
with m the smallest integer greater than max(al_1,...,al_Q). The problem is solved by means of the implicit product-integration rule of rectangular type having order 1 of convergence.
Further information on this code are available in the following paper
 Garrappa R.: Numerical Solution of Fractional Differential Equations: a Survey and a Software Tutorial, Mathematics 2018, 6(2), 16 doi: https://doi.org/10.3390/math6020016
downloadable pdf: http://www.mdpi.com/2227-7390/6/2/16/pdf
Roberto Garrappa (2021). Solving Multiterm Fractional Differential Equations (FDE) (https://www.mathworks.com/matlabcentral/fileexchange/66603-solving-multiterm-fractional-differential-equations-fde), MATLAB Central File Exchange. Retrieved .
Very good ! but i have a question? Can i put this FDE solver into the simulation environment?especially for simscape electricity?
Recently,i try to build some mechanical model and simulation including fractional differential equation in time domain.The ODEs cannot fulfill the needs.
@Sheldon Park: I got the same issue, then by following the guidance of Roberto Garrappa, I use smaller step-size then I worked.
However, fde12 can run with alpha > 0.8, if alpha < 0.8 then I have to use step-size h < 2^(-20) or so, which finally caused an error because of too small step-size.
@Roberto Garrappa: could you check your fde12 again using smaller fractional-orders such as alfa =0.02 or so? I believe it will get problems with small orders.
@Sheldon Park: different codes implement different methods, thus differences are normal. Ode23t.m is a variable step-size method which better treats the stiffness of your system close to the initial point. fde12 implements a substantially explicit method with fixed step-size and the step-size you selected is not sufficient to obtain a stable behavior. A smaller step-size, for instance h=2^(-10), surely may help. I strongly recommend to carefully read the description of the method and his properties (reported in the code and in the referenced papers) before using the code. A final question: why posting this comment here whilst it is related to the code http://www.mathworks.com/matlabcentral/fileexchange/32918-predictor-corrector-pece-method-for-fractional-differential-equations ?
Thanks for contributing fde12. I'm trying to solve a set of coupled equations containing fractional derivatives. To validate that I'm using it correctly, I tested on a simple problem using ODE and fde12 (with alpha=1.0). I would have expected the same result. Unfortunately, they don't. The ODE output makes sense but fde12 output blows up quickly. I'm not sure if I'm using it correctly. Any advice you can provide would be greatly appreciated. Thank you. -Sheldon
Here's the reaction I'm solving:
A + B < ---- > AB (kon=forward, koff=backward)
| k_el (rate of elimination for B)
The code I'm running is:
k_el = 1.7;
kon = 100;
koff = 2.5;
% function definition
myfun = @(t,y) [-kon*y(1)*y(2) + koff*y(3);
-kon*y(1)*y(2) + koff*y(3) - k_el*y(2);
kon*y(1)*y(2) - koff*y(3)];
% using ODE
tspan = [0, 50];
tic; sol = ode23t(myfun,tspan,[4;2.5;0]); toc;
figure(1); plot(sol.x,sol.y); legend; grid;
% using fde12
tic; [t, qsol]=fde12(alpha,myfun,t0,tfinal,[4;2.5;0],h); toc;
figure(2); plot(t,qsol(1,:)); legend; grid;
I request any one to give me any idea to solve fractional differential equations with delay. My personal email id is firstname.lastname@example.org
Respected @Roberto Garrappa
Thank you very much for your kind reply, I am very much happy to communicate with such a helping minded person. Now, I am able to solve fractional order differential equations by Matlab. I request you to give me an idea to solve fractional delay differential equations. If possible kindly give me some sample codes, since i am little bit poor in Matlab.
Thanks in advance.
@Roberto Garrappa Sir, please tell me how to solve FODE backward in time using your code? Please guide me sir.
Thank you in advance.
Dear P. Tamilalagan you can find other codes for FDEs in my mathworks author profile www.mathworks.com/matlabcentral/profile/authors/2361481-roberto-garrappa or in my web-page https://www.dm.uniba.it/Members/garrappa/Software
I need Matlab code for fractional differential equations, I require any suggestion or idea. Could you help me?
As clearly explained the code is devised for multi-term fractional differential equations and not for fractional differential equations with delay.
do the Matlab code for delayed fractional-order differential equations ?
very good function to solve an multi-term fractional-order differential equation. Well done Roberto!
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