Numerical solutions of the time dependent fractional order klein-gordon equation with finite difference method

This thesis consists of five chapters. The first chapter, which serves as an introduction, provides general information about the concept of fractional order analysis and the Klein-Gordon equation, along with references to some studies in the literature. The second chapter briefly covers the basic definitions and concepts required for the construction and progress of the study. The third and fourth chapters are devoted to the time-dependent fractional-order Klein-Gordon equation, which forms the core of the thesis. In the third chapter, the model problem is introduced, and explicit, implicit, and Crank-Nicolson finite difference schemes are developed, along with a stability analysis. The fourth chapter is devoted to solutions obtained using numerical methods. The solutions obtained using the methods presented in this chapter are compared with existing solutions in the literature in tables and graphs. The final chapter, the fifth chapter, deals with conclusions and recommendations.