Generalization of Fractional Kinetic Equations Containing Incomplete I-Functions*

Jangid, Kamlesh; Meena, Sapna; Bhatter, Sanjay; Purohıt, Sunıl Dutt

doi:10.1201/9781003263517-8

Cited by 2 publications

(1 citation statement)

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“…The Atangana–Baleanu fractional operator is also used to solve the fractional heat transfer model. Jangid et al [18] established a new model for a fractionalized kinetic equation using the Laplace transform (LT). Bhatter et al [19] investigated the Fredholm‐type integral family of equations with an incomplete

I

function using Mellin transformation and fractional calculus.…”

Section: Introductionmentioning

confidence: 99%

Fractional differential equations related to an integral operator involving the incomplete I‐function as a kernel

Bhatter

Kumawat

Jangid

et al. 2023

Math Methods in App Sciences

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In this study, we present and examine a fractional integral operator with an ‐function in its kernel. This operator is used to solve several fractional differential equations (FDEs). FDE has a set of particular cases whose solutions represent different physical phenomena. Much mathematical physics, biology, engineering, and chemistry problems are identified and solved using FDE. We first solve the FDE and the integral operator for the incomplete ‐function (I F) for the generalized composite fractional derivative (GCFD). This is followed by the discovery and investigation of several important exceptional cases. The significant finding of this study is a first‐order integer‐differential equation of the Volterra type that clearly describes the unsaturated nature of free‐electron lasers.

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