Solve Schrodinger Fractional Order Boundary Value Problem by Laplace Transformation Method

Asymmetry plays a significant role in the transmission dynamics of novel fractional calculus. Few studies have mathematically modeled such asymmetry properties, and none have developed Schrödinger models that incorporate different symmetry developmental stages. The Laplace transform, which can be used to discover the analytic (exact) solution to linear fractional differential equations. It is suggested in this work as a technique for resolving the fractional order Schrödinger equation with boundary conditions where the fractional derivatives of Caputo and Riemann-Liouville are applied. This can be used to resolve fractional and ordinary differential equations. After that, discovered the precise solution to a specific fractional differential equation example. The results show that the novel transform "Laplace Transform" when applied to the provided fractional differential equations boundary value problem, yields accurate solutions without the need for lengthy calculations. In this study, we investigate a class of fractional boundary value problems with two boundary value conditions that involve orders of fractional derivative: σ∈ (2,3] and x ∈ (0, a]. We illustrate our primary findings with several cases. We provide multiple examples to highlight our main conclusions. We proved the solution using the Laplace transformation after obtaining the existence using the fractional integral and integral operator methods.