Analysis of Fractional-Order Physical Models via Shehu Transform

In this study, an innovative analytical analysis of fractional-order partial differential equations is presented by Shehu transformation method. Fractional-order differential equations provide the useful dynamics of phys- ical systems and thus provide novel and efficient information about given physical systems. In this study, Shehu transform is used to create an approximate analytical solution through the time-fractional partial differential equations (system of equations) with the Adomian decomposition method and Variational iter- ation transform method along with Shehu transformation. Laplace and Sumudu transformation have been refined to form Shehu transformation. An algorithm is established for expressing the Shehu transform for the fractional operators like Riemann-Liouville and Caputo by using this new integral transform. Higher-order fractional differential equations are solved in the Caputo sense. Shehu transformation is used to simplify the problems before implementing the decomposition and variational iteration methods to achieve the problem’s comprehensive solutions. This method provides a series form solution with easily computed components and a higher rate of convergence to the exact solution of the targeted problem. The reliability of this process is demonstrated through physical problems. MATLAB software is used to analyze the problems graphically. It is observed that integer-order differential equations do not properly model various phenomena in different fields of science and engineering in relation to fractional-order differential equations. This method is simple and accurate analytical technique that can solve other partial differential equations of fractional order as well.