Analytical Approximate Solutions of Nonlinear Fractional-Order Nonhomogeneous Differential Equations

Computational simulation of natural phenomenon is currently attracting increasing interest in applied mathematics and computational physics. Mathematical software for simulation is limited by the availability, speed, and parallelism of high-performance computing. To improve the performance and efficiency of some numerical techniques, a step-by-step approach to mathematical software coding is needed to build robust parameter-oriented problems. Therefore, this article aims to present and apply the Adomian decomposition algorithm coded by the MAPLE 18 software package for the solutions of nonlinear fractional-order differential equations in applied physics and engineering sciences. The present technique is used without linearization or slight disturbance of nonlinear terms, which confirms the strength, accuracy, and simplicity of the algorithm. The two test problems are considered for different initial conditions and the solutions obtained show that the Adomian decomposition algorithm is fast, easy, stable in good agreement with analytical techniques and that a good computational approach to fractional-order value problems arising in applied mathematics and engineering sciences.