TY - JOUR
ID - 16770
TI - Numerical solution for a class of variable order fractional integral-differential equation with Atangana-Baleanu-Caputo fractional derivative
JO - Journal of Advanced Mathematical Modeling
JA - JAMM
LA - en
SN - 2251-8088
AU - Mohammadinejad, Hajimohammad
AU - Khosravi, Hassan
AD - Department of Mathematics, Faculty of Science, University of Birjand, Birjand, Iran.
Y1 - 2021
PY - 2021
VL - 11
IS - 2
SP - 253
EP - 270
KW - Atangana-Baleanu-Caputo fractional derivative
KW - Chebyshev polynomials
KW - Operational matrixes
KW - Fractional integral-differential equations
DO - 10.22055/jamm.2021.35430.1866
N2 - 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.
UR - https://jamm.scu.ac.ir/article_16770.html
L1 - https://jamm.scu.ac.ir/article_16770_e5f0394a0f53e68e822dbf4f66207d02.pdf
ER -