On the Numerical Evaluation for Studying the Time Fractional Partial Delay Differential Equations

An important challenge in mathematical modeling is to find a model that captures the fundamental physics of a system and is simple enough to allow for mathematical analysis. In the physical sciences, physiology, ecology, and other practical research domains, fractional delay differential equations (FDDEs) are frequently used. Most fractional delay differential equations can only be solved numerically because they lack analytic solutions. In contrast to the Adomian decomposition method, a new method for solving delay differential equations called the new Fractional Novel Analytical Scheme (FNAS) is presented in this paper. A fractional novel analytical scheme is built on the fractional Taylor series. The calculation is done using the Caputo derivative. Three well-known physical models such as advection-dispersion equation of fractional-order, nonlinear gas-dynamics equation of fractional-order and convection-diffusion equation of fractional-order with proportional time-delay are solved by using the proposed technique to demonstrate the performance and efficiency of the FNAS. By graphing absolute error values and contrasting results to numerous existing solutions, the correctness of the proposed technique is presented. In addition to being straightforward, the suggested strategy is accurate and logical in the difficulties it solves.