Analytical and Numerical Methods for Solving Second-Order Two-Dimensional Symmetric Sequential Fractional Integro-Differential Equations

In this paper, we investigate the solution to a class of symmetric non-homogeneous two-dimensional fractional integro-differential equations using both analytical and numerical methods. We first show differences between Caputo derivative sequential how they help facilitate implementation approaches. Then, propose approach based on operational matrix method, which involves deriving matrices for differential integral terms equation combining them generate single algebraic system. This method allows efficient accurate approximation without need projection. Our findings demonstrate effectiveness solving equations. then provide examples test our method. The results accuracy efficiency approach, with graph exact approximate solutions showing almost complete overlap, problem converges integer as order approaches one. use various methods measure error in approximation, such absolute L2 errors. Additionally, explore effect order. that is 10−14, while 10−13. Next, apply Laplace transform find an extend case. consider all homogeneous cases. Through examples, achieve two purposes. First, obtained are implemented, especially some 1D 2D classes. ordinary