%0 Journal Article
%T Numerical solution for a class of variable order fractional integral-differential equation with Atangana-Baleanu-Caputo fractional derivative
%J Journal of Advanced Mathematical Modeling
%I Shahid Chamran University of Ahvaz
%Z 2251-8088
%A Mohammadinejad, Hajimohammad
%A Khosravi, Hassan
%D 2021
%\ 06/22/2021
%V 11
%N 2
%P 253-270
%! Numerical solution for a class of variable order fractional integral-differential equation with Atangana-Baleanu-Caputo fractional derivative
%K Atangana-Baleanu-Caputo fractional derivative
%K Chebyshev polynomials
%K Operational matrixes
%K Fractional integral-differential equations
%R 10.22055/jamm.2021.35430.1866
%X In this paper we consider fractional integral-differential equations of variable order containing Atangana-Baleanu-Caputo fractional derivatives as follows: \begin{align*} \mathfrak{D}_{\alpha(t)}^{ABC}&\Big[u(x,t).g(x,t)\Big]+\frac{\partial u(x,t)}{\partial t}+\int_{0}^{t}u(x,Y)dY\nonumber\\ &+\int_{0}^{t}u(x,Y).k(x,Y)dY=f(x,t), \end{align*} We try to solve this equation using a numerical method based on matrix operators including Chebyshev polynomials. By using these operational matrixes the fractional order integral-differential equation is transformed into an algebraic system which by solving them, we will obtain the numerical answer of the above fractional integral-differential equation. To show the accuracy and efficiency of this method, we have calculated some numerical examples by MATLAB software.
%U https://jamm.scu.ac.ir/article_16770_e5f0394a0f53e68e822dbf4f66207d02.pdf