Existence and numerical solutions of a coupled system of integral BVP for fractional differential equations

• Main Authors: Kamal Shah, Jinrong Wang, Hammad Khalil, Rahmat Ali Khan
• Format: Article
• Language: English
• Published: SpringerOpen 2018-04-01
• Series: Advances in Difference Equations
• Subjects: Fractional differential system; Integral boundary value problem; Numerical solutions; Differential transform; Hyers–Ulam stability
• Online Access: http://link.springer.com/article/10.1186/s13662-018-1603-1

Abstract This paper is devoted to establishing the existence theory for at least one solution to a coupled system of fractional order differential equations (FDEs). The problem under consideration is subjected to movable type integral boundary conditions over a finite time interval. Furthermore, we investigate the approximate solutions to the considered problem with the help of the differential transform. Moreover, some necessary conditions for the Hyers–Ulam type stability to the solution of the proposed problem are developed. The whole investigation has been illustrated by providing some suitable examples.