APPLICATION OF THE SOME BLAISE ABBO METHOD (SBA) FOR SOLVING THE NONLINEAR FRACTIONAL SCHRÖDINGER EQUATIONS
Keywords:
SBA method, differential equation, fractional Schrödinger equationDOI:
https://doi.org/10.17654/0975045225012Abstract
We present the analytical study of time-fractional nonlinear Schrödinger equation arising in various fields of science and engineering, where the order of fractional time derivate parameter $\alpha$ varies between $0<\alpha<1$. New version of Some Blaise Abbo method is incorporated to solve the time-fractional nonlinear Schrödinger equation, where the fractional derivates are taken in Caputo sense, and the fractional integral in Riemann-Liouville sense with $0<\alpha<1$, $1<\alpha \leq 2$. Two types of time-fractional nonlinear Schrödinger equation are tackled in the present research. This method obtains its results through a series of successive iterations, and the resulting form rapidly converges to the exact solution. The results obtained via new version Some Blaise Abbo method show that this scheme is easy authentic, effective, and simple for nonlinear fractional PDEs. Some graphical structures are displayed at different levels of fractional orders using Matlab software. The new version of Some Blaise Abbo method will surely help to determine the analytical solution to some complex fractional PDEs as well as integro-differential equations.
Received: December 11, 2024
Revised: February 5, 2025
Accepted: February 19, 2025
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