Certain generalized fractional calculus formulas and integral transforms involving $(p,q)$-Mathieu-type series

Agarwal, Ravi P.; Kılıçman, Adem; Parmar, Rakesh K.; Rathie, Arjun K.

doi:10.1186/s13662-019-2142-0

Cited by 4 publications

(3 citation statements)

References 7 publications

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“…The general pair of fractional integral operators so-called Marichev-Saigo-Maeda(M-S-M) involving the third Appell's function of two-variables F 3 (.) are defined by (see, for details, [1,11,18,19,20]). Definition 1.…”

Section: Introductionmentioning

confidence: 99%

CERTAIN GENERALIZED FRACTIONAL CALCULUS FORMULAS AND INTEGRAL TRANSFORMS OF (p, q)-EXTENDED τ -HYPERGEOMETRIC FUNCTION

Gupta¹,

Modi²,

Jha³

et al. 2022

SEAJMMS

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In this paper, we established certain image formulas of the (p, q)–extended τ hypergeometric function Rτ p ,q (a, b; c; z) by employing Marichev-Sigo-Maeda(M-S-M) fractional integration and differentation Corresponding special cases for the Saigo’s, Riemann-Liouville and Erdelyi-Kober fractional integral and differ- ential operators are also deduced which are earlier obtained by Solanki et al. [23]. Further certain integral transforms of the (p, q)–extended τ hypergeometric function Rτ (a, b; c; z) are established. All the results are represented in terms of the Hadamard product of the (p, q)–extended τ hypergeometric function Rτ (a, b; c; z) and the Fox-Wright function.

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Section: Introductionmentioning

confidence: 99%

CERTAIN GENERALIZED FRACTIONAL CALCULUS FORMULAS AND INTEGRAL TRANSFORMS OF (p, q)-EXTENDED τ -HYPERGEOMETRIC FUNCTION

Gupta¹,

Modi²,

Jha³

et al. 2022

SEAJMMS

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“…Numerus problems of interests from these fields can be analyzed through the fractional integrals, which can also be regarded as an interesting sub-discipline of fractional calculus. Some of the applications of integral calculus can be seen in the following papers [5,6,7,8], through which problems in physics, chemistry and population dynamics were studied. The fractional integrals were extended to include the Hermite-Hadamard type inequalities, which are classically given as follows.…”

Section: Introductionmentioning

confidence: 99%

Integral Inequalities for s-Convexity via Generalized Fractional Integrals on Fractal Sets

Almutairi

Kılıçman

2020

Mathematics

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In this study, we establish a new integral inequalities of Hermite-Hadamard type for s-convexity via Katugampola fractional integral. This generalizes the Hadamard fractional integrals and Riemann-Liouville into a single form. We show that the new integral inequalities of Hermite-Hadamard type can be obtained via the Riemann-Liouville fractional integral. Finally, we give some applications to special means.

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“…al. [6], [1] defined its inverse and studied some additional fundamental properties of this transform and named it the Natural transform.…”

Section: Introductionmentioning

confidence: 99%

A Note on Natural Transformation of Exton’s Triple Series Hypergeometric Function

Harsh¹,

Sharma²,

Khan³

2020

Nep J. Math. Sci.

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Triple series hypergeometric functions are very important from the applications point of view. Exton had defined 20 triple hypergeometric functions namely X1 , X2 , … , X20. Integral transform technique is widely using for research purpose. Natural transform is a new kind of integral transform and generalization of Laplace transform. In the present research note, we give the Natural integrals of the triple series hypergeometric function due to Exton.

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Certain generalized fractional calculus formulas and integral transforms involving $(p,q)$-Mathieu-type series

Abstract: In this paper, we establish sixteen interesting generalized fractional integral and derivative formulas including their composition formulas by using certain integral transforms involving generalized (p, q)-Mathieu-type series. MSC: Primary 26A33; 33B15; secondary 3C05; 33C99; 44A10

Cited by 4 publications

References 7 publications

CERTAIN GENERALIZED FRACTIONAL CALCULUS FORMULAS AND INTEGRAL TRANSFORMS OF (p, q)-EXTENDED τ -HYPERGEOMETRIC FUNCTION

CERTAIN GENERALIZED FRACTIONAL CALCULUS FORMULAS AND INTEGRAL TRANSFORMS OF (p, q)-EXTENDED τ -HYPERGEOMETRIC FUNCTION

Integral Inequalities for s-Convexity via Generalized Fractional Integrals on Fractal Sets

A Note on Natural Transformation of Exton’s Triple Series Hypergeometric Function

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