A Study on Fuzzy Fractional Equation using Laplace Transform in Quantum environment
DOI:
https://doi.org/10.30495/jme.v18i0.2847Keywords:
Fuzzy Fractional Calculus, Quantum Calculus, $q$-Laplace transform, $q$-Mittag-Leffler, Hyers-Ulam-Rassias Stability.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.Downloads
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