Residual Methods For Solving Fractional Differential Equations With Singular Kernels - Abuomar, Mohammed M. A. (2023)
In this thesis, we implement two residual methods to solve two important fractional applications in science and engineering. The fractional derivative is used in the Caputo sense. For this reason, we start this study by discussing and providing several properties of fractional calculus. Comprehensive study for the theory of fractional calculus are presented. The first residual method used in this thesis is a combination of fractional series method and fractional Laplace transform method. This combination is use to solve an important application in physics which is the fractional diffusion-wave equation with a reaction. The main purpose of this method is to solve this problem analytically.