Fractional-Order Partial Differential Equation with Proportion Delay and Sumudu Decomposition Method

In this work we consider the new approach which is more accurate to obtain the solution of fractional order partial differential equations (FPDEs) with proportional delay, including generalized Burger equation partial differential equation and telegraph partial differential equation with proportional delay. Integral order is obtained in series form to show the convergence of the method, illustrative examples are considered to confirm the validity and applicability of the method. By converting the fractional delay differential equation into a set of algebraic equations, this approach makes it possible to derive an infinite series solution that comes close to the exact solution. The original fractional delay differential equations approximate analytical solution converges to this infinite series solution. When it comes to solving FPDEs with proportionate delay a class of problems for which analytical solutions are notoriously hard to find the Sumudu Adomian decomposition method (SADM) is commended for its simplicity, efficacy and correctness.