Numerical Solutions Caused by DGJIM and ADM Methods for Multi-Term Fractional BVP Involving the Generalized <i>ψ</i>-RL-Operators

Abstract

In this research study, we establish some necessary conditions to check the uniqueness-existence of solutions for a general multi-term ψ-fractional differential equation via generalized ψ-integral boundary conditions with respect to the generalized asymmetric operators. To arrive at such purpose, we utilize a procedure based on the fixed-point theory. We follow our study by suggesting two numerical algorithms called the Dafterdar-Gejji and Jafari method (DGJIM) and the Adomian decomposition method (ADM) techniques in which a series of approximate solutions converge to the exact ones of the given ψ-RLFBVP and the equivalent ψ-integral equation. To emphasize for the compatibility and the effectiveness of these numerical algorithms, we end this investigation by providing some examples showing the behavior of the exact solution of the existing ψ-RLFBVP compared with the approximate ones caused by DGJIM and ADM techniques graphically.

Keywords

• ADM numerical method
• DGJIM numerical method
• boundary value problem
• existence