A Study on Fuzzy Fractional Equation using Laplace Transform in Quantum environment

Abstract

The primary goal of this research is to solve the fuzzy-valued initial value problem under Caputo q-fractional sense and analyse its stability. Quantum calculus often known as q-calculus, is a modern discipline which is growing in several fields and includes limitless calculations. It is a mathematical framework devised to explain the behavior of the quantum mechanics field. The Caputo q-fractional equation is solved in this study by incorporating it with the fuzzy fractional calculus. The solution to the Caputo q-fractional differential equation is determined using the q-Laplace transform and the q-Mittag Leffler. Additionally, the fuzzy valued function is employed in the Caputo q-fractional differential equation, which is then solved using the q-Laplace transform. The numerical examples are solved using the q-Laplace transform, and they are shown graphically. Finally, the Hyers-Ulam-Rassias stability of the fractional differential equation is addressed.