المحاكاة العددية لبعض المعادلات التفاضلية ذات الرتب الكسرية المتغيرة

Abstract

Thesis Title: Numerical Simulations for Some Variable Order Fractional Differential Equations. This thesis is a contribution on numerical studies for fractional variable order differential equations. The primary purpose of this research is to implement numerical study of the variable order fractional wave model by the weighted average finite difference methods. The wave variable order fractional differential equation (WVOFDE) is studied by the weighted average finite difference methods (WAFDM), where the order of the derivative is a function of time. The concept of the fractional derivative in this thesis is considered in the sense of Riemann-Liouville variable order fractional derivative for the time derivative. Moreover, we introduced some variable order differential models. Theorem with their proof are presented by using a kind of Von Neumann analysis to study the stability of the proposed finite difference schemes. To explore that the method is effective, some numerical examples are offered. Finally, the obtained results are compared with the exact solutions.