Bivariate Chebyshev polynomials of the fifth kind for variable-order time-fractional partial integro-differential equations with weakly singular kernel

Advances in Difference Equations

Dumitru Baleanu¹  Kamyar Hosseini²  Khadijeh Sadri²  Soheil Salahshour³  Ali Ahmadian⁴ 

[1] Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530, Ankara, Turkey;Institute of Space Sciences, R 76900, Magurele-Bucharest, Romania;Department of Medical Research, China Medical University, 40447, Taichung, Taiwan;Department of Mathematics, Rasht Branch, Islamic Azad University, P.O. Box. 41335-3516, Rasht, Iran;Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey;Institute of IR 4.0, The National University of Malaysia, 43600, Bangi, Selangor, Malaysia;

关键词: Variable-order time-fractional weakly singular partial integro-differential equations;    Pseudo-operational matrix;    Fifth-kind Chebyshev polynomials;    Caputo derivative;    Riemann–Liouville integral;    35Q80;    45D05;    45E10;    45K05;    45K05;   

DOI  :  10.1186/s13662-021-03507-5

来源: Springer

【 摘 要 】

The shifted Chebyshev polynomials of the fifth kind (SCPFK) and the collocation method are employed to achieve approximate solutions of a category of the functional equations, namely variable-order time-fractional weakly singular partial integro-differential equations (VTFWSPIDEs). A pseudo-operational matrix (POM) approach is developed for the numerical solution of the problem under study. The suggested method changes solving the VTFWSPIDE into the solution of a system of linear algebraic equations. Error bounds of the approximate solutions are obtained, and the application of the proposed scheme is examined on five problems. The results confirm the applicability and high accuracy of the method for the numerical solution of fractional singular partial integro-differential equations.

【 授权许可】

CC BY