Analytical Approach for Solution of Linear and Non-linear Time-Fractional Schrödinger’s Equations by Employing Sumudu Transform Iterative Method

In the present research paper, an iterative approach named the Sumudu transform method is implemented to solve the time-fractional Schrödinger equations in one, two, and three dimensions respectively. In literature, rarely all dimensions are tackled regarding time-fractional Schrödinger equations. In the present research, iterative Sumudu transform is implemented for the semi analytical solutions. These equations are the prominent ones in the field of quantum physics and in some other significant problems. The efficacy and authenticity of the proposed method are tested by the comparison of approximated and exact results in graphical form. 2 D and 3 D plots are provided to affirm the compatibility of the approximated-exact results. Sumudu transform is a reliable and efficient tool to provide the approximated and exact result to a vast class of ODEs, PDEs, and fractional PDEs in a simplified way, without any discretization, linearization and is free of errors. Convergence analysis is also provided regarding this research. The main highlights of this research done are linked to the convergence and the graphical claim of compatibility between approx. and analytical approximations. With aid of the developed regime, it is affirmed that this regime has full potential to generate the fast-converging solutions. With the aid of this research focus is regarding numerical convergence of results and the compatibility of solutions. The developed regime would be a major breakthrough in the field of finding semi analytical approximations for complex natured fractional PDEs. © 2023, The Author(s), under exclusive licence to Springer Nature India Private Limited.