Solution of Bicomplex Time Fractional Schrödinger Equation Involving Bicomplex Mittag-Leffler Function

In this paper, we investigate the bicomplex Schrödinger’s equation of fractional order and derive its solution via Euler identity. The first order time derivative of the bicomplex Schrödinger’s equation is changed into a Caputo fractional derivative, resulting in the time fractional Schrödinger’s equation. The Euler identity for the bicomplex Mittag-Leffler function has been established and is being utilized to solve the bicomplex time fractional Schrödinger’s equation. The bicomplex time fractional Schrödinger equation is solved for a free particle and a potential well and the answer is represented in terms of the bicomplex Mittag-Leffler function. There are both hyperbolic and complex numbers in the bicomplex numbers. Through research in the bicomplex space, the results that are created independently for these can be brought together.