Analytical and numericaltreatment of nonlinear fractional differential equations involving caputo fractional operator

Abstract

Nonlinear fractional differential equations play an important role in applied mathematics and physics. It is difficult to obtain the exact solution for these problems due to the complexity of the nonlinear terms included. In recent decades, there has been great development in the numerical analysis and exact solution for nonlinear fractional differential equations. The main objective of this thesis is to study the solutions of nonlinear fractional differential equations involving Caputo fractional operator by proposing new technique. To demonstrate the validity and reliability of this technique, it is applied to several numerical examples.