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.
