The Impact on Raise of Environmental Pollution and Occurrence in Biological Populations Pertaining to Incomplete H-function

In this paper, we assess an integral containing incomplete H-functions and utilize it to build up an expansion formula for the incomplete H-functions including the Bessel function. Next, we evaluate an integral containing incomplete H̅-functions and use it to develop an expansion formula for the incomplete H̅-functions including the Bessel function. The outcomes introduced in this paper are general in nature, and several particular cases can be acquired by giving specific values to the parameters engaged with the principle results. As particular cases, we derive expansions for the incomplete Meijer ${}^{(\Gamma )}G$ G ( Γ ) -function, Fox–Wright ${}_{p}\Psi _{q}^{(\Gamma )}$ Ψ q ( Γ ) p -function, and generalized hypergeometric ${}_{p}\Gamma _{q}$ Γ q p function.

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“…Now applying (22) and the orthogonality property of the Bessel functions [17, p. 291, (6)], we obtain…”

Section: Theorem 31 Let Hmentioning

confidence: 99%

Some expansion formulas for incomplete H- and H̅-functions involving Bessel functions

et al. 2020

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“…A few applications are also presented. Furthermore, the incomplete

H

‐function and I

I

F have been observed in various response‐related problems, including diffusion, reaction‐diffusion, electronics and connectivity, fractional differential equations (FDEs), and a variety of other areas of physics, biology, and probability theory, to name a few [12–16]. The Atangana–Baleanu fractional operator, which is a fractional‐order derivative, was proposed by Atangana and Baleanu [17].…”

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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“…Mathematical modelling appears to be the expression of physical systems through comprehensible mathematical equations, the theoretical and computational study of which provides constructive interpretation, clarification, and direction for the application that occurs. The authors [1,2,[5][6][7][8][9][10][11][12]14] have demonstrated the utility of mathematical models of various fluid problems, biological problems, electrical elements, and systems in describing complex phenomena over the last few decades.…”

Section: Introductionmentioning

confidence: 99%

A study of the RLC, RC, and RL electric circuits associated with incomplete I-functions

Jangid

Nishant

Samei

et al. 2022

Preprint

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The Impact on Raise of Environmental Pollution and Occurrence in Biological Populations Pertaining to Incomplete H-function

Cited by 19 publications

References 12 publications

Some expansion formulas for incomplete H- and H̅-functions involving Bessel functions

Some expansion formulas for incomplete H- and H̅-functions involving Bessel functions

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

A study of the RLC, RC, and RL electric circuits associated with incomplete I-functions

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