A new approach to approximate solutions for a class of nonlinear multi-term fractional differential equations with integral boundary conditions

Abstract

Abstract In this paper, we discuss the existence and uniqueness of solutions for a class of integral boundary value problems of nonlinear multi-term fractional differential equations and propose a new method to obtain their approximate solutions. The existence results are established by the Banach fixed point theorem, and approximate solutions are determined by the Daftardar-Gejji and Jafari iterative method (DJIM) and the Adomian decomposition method (ADM). Finally, we present some examples to illustrate the existence result and the effectiveness of applied approximate techniques.

Keywords

• Fractional differential equation
• Integral boundary condition
• Banach fixed point theorem
• Daftardar-Gejji and Jafari iterative method
• Adomian decomposition method