Certain integral transforms concerning the product of family of polynomials and generalized incomplete functions

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

doi:10.2478/mjpaa-2020-0019

Cited by 5 publications

(3 citation statements)

References 21 publications

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“…Ever after Jackson [3] presented the q-integral concept, various q-analogues of various types of integral transforms were given in a classical way (see, e.g., [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]). Consisting of the notion of regular operators [20], the theory of Boehmians was first introduced by [21] to generalize distributions and regular operators [22] (see, e.g., [21,[23][24][25][26][27][28][29][30][31]).…”

Section: Preliminariesmentioning

confidence: 99%

The q-Sumudu transform and its certain properties in a generalized q-calculus theory

Al‐Omari

2021

Adv Differ Equ

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In this paper we consider a generalization to the q-calculus theory in the space of q-integrable functions. We introduce q-delta sequences and develop q-convolution products to derive certain q-convolution theorem. By using the concept of q-delta sequences, we establish various axioms and set up q-spaces of generalized functions named q-Boehmian spaces. The new assigned spaces of q-generalized functions are acceptable and compatible with the classical spaces of the ordinary functions. Consequently, we extend the generalized q-Sumudu transform to the sets of q-Boehmian spaces. On top of that, we nominate the canonical q-embeddings between the q-integrable sets of functions and the q-integrable sets of q-Boehmians. Furthermore, we address the general properties of the generalized q-Sumudu transform and its inversion formula in some detail.

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Section: Preliminariesmentioning

confidence: 99%

The q-Sumudu transform and its certain properties in a generalized q-calculus theory

Al‐Omari

2021

Adv Differ Equ

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“…The incomplete H-functions mentioned in equations [4] and [6] are valid for all 𝑦 ≥ 0 under the similar contour and the same conditions specified in (7). Some Special Cases of Incomplete H-Functions (i) Specializing 𝑦 = 0 in [6], reduces the incomplete H-function Γ , , (𝑧) to Fox's H-function (refer (8)).…”

Section: Introductionmentioning

confidence: 99%

Inverse Laplace Transform of the Incomplete H-Function

Ghiya¹,

Sridevi²,

Manjula³

2022

ECS Trans.

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Special functions have enormous applications in theoretical and applied mathematics. This field is constantly expanding and addressing new problems in engineering applications and applied sciences. H-function one and more variables have been applied in large range of areas, such as electronics and communication, astrophysics, fractional differential equations, super statistics, diffusion, reaction–diffusion, and other fields like probability theory, biology, and theoretical physics. Some situations of heat conduction and astrophysics problems are not adequately addressed by basic category of special functions. To address such problems, incomplete special functions found the way in the literature. Incomplete H-functions are attracting researchers working on heat conduction and astrophysics problems. The paper aims to transform the products of algebraic powers and incomplete H-function in another domain using inverse laplace transform. Results are obtained in terms of the incomplete H-function as compact form. Further, some particular cases are mentioned by giving special values to the incomplete H-function’s parameters.

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“…Recently, Bansal et al [4,5,6,7] discussed about some of the new outcomes and uses of the incomplete H-functions; such as they solved the Fredholm-type integral equation involving incomplete H-function and incomplete H-function in the kernel, useful classical integral transforms of the ℵ-functions, some new outcomes of Srivastava-Luo-Raina M-transform associated to incomplete H-function, and Oberhettinger's integral formula involving M-series. Recent studies [8,9,10,11] for further details on the characteristics of incomplete I-functions.…”

Section: Introductionmentioning

confidence: 99%

Certain expansion formulae of incomplete $I$-functions associated with the Leibniz rule

Meena

Bhatter

Jangid

et al. 2021

J Frac Calc & Nonlinear Sys

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Certain integral transforms concerning the product of family of polynomials and generalized incomplete functions

Cited by 5 publications

References 21 publications

The q-Sumudu transform and its certain properties in a generalized q-calculus theory

The q-Sumudu transform and its certain properties in a generalized q-calculus theory

Inverse Laplace Transform of the Incomplete H-Function

Certain expansion formulae of incomplete $I$-functions associated with the Leibniz rule

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