Daftar-Gejii and Jafaris Method for Non-Linear Third Order Fractional Diifferential Equation

Abstract

Partial differential equations (PDEs) play a crucial role in modeling various phenomena in science and engineering, involving multiple independent vari ables and their partial derivatives. Fractional calculus extends the concepts of differentiation and integration to non-integer orders, providing a powerful tool for studying physical phenomena with memory-like properties. Fractional partial differential equations (FPDEs) involve fractional derivatives and have applications in diverse fields. This thesis focuses on the numerical solution of third-order FPDEs using the Daftar-Gejii-Jafaris (DGJ) method. The DGJ method, a relatively new mathematical tool, has shown promise in solv ing differential equations. However, its application to FPDEs remains under explored. The research aims to bridge this gap by investigating the DGJ method’s efficiency in solving non-linear third-order FPDEs. The objectives of the study include applying the DGJ method to solve third-order FPDEs, illustrating solutions for specific non-linear cases, and describing the solu tions graphically. The study’s significance lies in contributing new concepts to the research in this area, providing reference material, and enhancing un derstanding of mathematical techniques for solving FPDEs. Numerical exam ples, including a non-linear third-order FPDE, are presented to demonstrate the DGJ method’s effectiveness. The results show that the DGJ method can accurately approximate solutions, providing a valuable contribution to the field of fractional calculus and differential equations.