روش عددی برای یک کلاس از معادله کسری انتگرال- دیفرانسیل کسری مرتبه متغییر با مشتقات کسری آتانگانا- بالینو-کاپوتو

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_{۰}^{t}u(x,Y)dY\nonumber\\ &+\int_{۰}^{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.

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مشتق کسری آتانگانا-بالینو-کاپوتو ، چند جمله ای چبیشف ، ماتریس های عملیاتی ، معادله انتگرال-دیفرانسیل کسری