Published Paper Details:

This Research paper focuses on fractional calculus expands the idea of differentiation & integration to non-integer orders. Fractional derivatives provide extra modelling degrees of freedom while integer-order derivatives are well-known and often employed. Applications for fractional derivative operators can be found in many disciplines, including signal processing, image analysis, physics, and engineering. To fully utilise the potential of fractional derivative operators across a range of domains, it is crucial to comprehend their basic notions. The concept of fractional calculus was first introduced in a set of letters sent in 1695. Leibniz responded to L'Hopital's query about what would occur if the order of differentiation were assumed to be 1/2, and he said it seems that these contradictions will eventually have beneficial ramifications. The symbol d^n/(dx^n ) f(x), created by Leibniz in the late seventeenth century, represents a function's n^th derivative, with the conclusion that n?N. De l'Hospital was informed of this and in response, he questioned the importance of the operator if n = 1/ 2. Although n need not be restricted to Q, for the purposes of this paper, n ? R applies to all operators in the following text. This branch of mathematics is known as fractional calculus because of the specific questioning of Leibniz's operator in relation to n = 1/ 2 (a fraction).