An efficient computational scheme for nonlinear time fractional systems of partial differential equations arising in physical sciences

Advances in Difference Equations

article

Dubey, Ved Prakash¹  Kumar, Rajnesh²  Kumar, Devendra³  Khan, Ilyas⁴  Singh, Jagdev⁵ 

[1] Faculty of Mathematical and Statistical Sciences, Shri Ramswaroop Memorial University;Department of Applied Science and Humanities, Government Engineering College, Dept. of Science and Technology;Department of Mathematics, University of Rajasthan;Faculty of Mathematics and Statistics, Ton Duc Thang University;Department of Mathematics, JECRC University

关键词: Mittag-Leffler function;    Residual power series method;    Partial differential equations;    Taylor function;    Residual error;   

DOI  :  10.1186/s13662-020-2505-6

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this paper, we broaden the utilization of a beautiful computational scheme, residual power series method (RPSM), to attain the fractional power series solutions of nonhomogeneous and homogeneous nonlinear time-fractional systems of partial differential equations. This paper considers the fractional derivatives of Caputo-type. The approximate solutions of given systems of equations are calculated through the utilization of the provided initial conditions. This iterative scheme generates the fast convergent series solutions with conveniently determinable components. The implementation of this numerical scheme clearly exhibits its effectiveness, reliability and easiness regarding the procedure of the solution, as well as its better approximation. The repercussions of the fractional order of Caputo derivatives on solutions are depicted through graphical presentations for various particular cases.

【 授权许可】

CC BY