Unified fractional integral and derivative formulas, integral transforms of incomplete $$\tau $$-hypergeometric function

Suthar, D. L.; Chandak, S.; Amsalu, Hafte

doi:10.1007/s13370-020-00848-4

Cited by 3 publications

(1 citation statement)

References 7 publications

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“…Readers can refer to [13][14][15][16][17][18][19][20] for more generalizations and extensions of extended fractional kinetic equations.…”

Section: Introductionmentioning

confidence: 99%

Solutions of Fractional Kinetic Equations using the $(p,q;l)$-Extended τ -Gauss Hypergeometric Function

Abubakar

2022

Journal of New Theory

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The main objective of this paper is to use the newly proposed $(p,q;l)$-extended beta function to introduce the $(p,q;l)$-extended $τ$-Gauss hypergeometric and the $(p,q;l)$-extended $τ$-confluent hypergeometric functions with some of their properties, such as the Laplace-type and the Euler-type integral formulas. Another is to apply them to fractional kinetic equations that appear in astrophysics and physics using the Laplace transform method.

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“…Readers can refer to [13][14][15][16][17][18][19][20] for more generalizations and extensions of extended fractional kinetic equations.…”

Section: Introductionmentioning

confidence: 99%

Solutions of Fractional Kinetic Equations using the $(p,q;l)$-Extended τ -Gauss Hypergeometric Function

Abubakar

2022

Journal of New Theory

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On the matrix versions of the k analog of ℑ‐incomplete Gauss hypergeometric functions and associated fractional calculus

Qadha,

Bakhet

2024

Math Methods in App Sciences

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In this paper, our aim is to introduce a new definition of ( ‐incomplete Wright hypergeometric matrix functions ( ‐IWHMFs) using the ‐incomplete Pochhammer matrix symbol. First, we define the ‐incomplete gamma matrix function and introduce the ‐incomplete Pochhammer matrix symbols. Furthermore, we present differential formulas and integral representation related to these ‐IWHMFs. We have also obtained some results regarding the ‐fractional calculus operators of these ‐IWHMFs. Finally, we investigate the solutions of fractional kinetic equations (FKEs) involving the ‐IWHMFs.

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A New Class of Extended Hypergeometric Functions Related to Fractional Integration and Transforms

Palsaniya

Mittal

Suthar

et al. 2022

Journal of Mathematics

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The focus of this research is to use a new extended beta function and develop the extensions of Gauss hypergeometric functions and confluent hypergeometric function formulas that are presumed to be new. Four theorems have also been defined under the generalized fractional integral operators that provide an image formula for the extension of new Gauss hypergeometric functions and the extension of new confluent hypergeometric functions. Moreover, discussed are analogous statements in terms of the Weyl, Riemann–Liouville, Erdélyi–Kober, and Saigo fractional integral and derivative operator types. Here, we are also able to generate more image formulas by keeping some integral transforms on the obtained formulas.

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Unified fractional integral and derivative formulas, integral transforms of incomplete $$\tau $$-hypergeometric function

Cited by 3 publications

References 7 publications

Solutions of Fractional Kinetic Equations using the $(p,q;l)$-Extended τ -Gauss Hypergeometric Function

Solutions of Fractional Kinetic Equations using the $(p,q;l)$-Extended τ -Gauss Hypergeometric Function

On the matrix versions of the k analog of ℑ‐incomplete Gauss hypergeometric functions and associated fractional calculus

A New Class of Extended Hypergeometric Functions Related to Fractional Integration and Transforms

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