Distributional Representation of a Special Fox-Wright Function with an Application

Article Mathematics

New Results Involving the Generalized Kratzel Function with Application to the Fractional Kinetic Equations

Asifa Tassaddiq et al.

Summary: A new fractional kinetic equation is formulated and solved in this article using generalized Kratzel integrals, as the nuclear reaction rate in astrophysics is represented in terms of these integrals. New identities involving the Fox-Wright function are discussed and used to simplify the results. Several new identities for a variety of classic fractional transforms are derived by utilizing Kiryakova's fractional integral and derivative operators with the Kratzel function. The relationship between the generalized Kratzel function and the H-function is analyzed. The closed form of the results is expressible in terms of the Mittag-Leffler function. The distributional representation and Laplace transform of the Kratzel function have played an essential role in achieving the goals of this work.

MATHEMATICS (2023)

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Article Mathematics, Interdisciplinary Applications

New Results Involving Riemann Zeta Function Using Its Distributional Representation

Asifa Tassaddiq et al.

Summary: The relationship between special functions and fractional integral transforms has a significant impact on scientific research, particularly the image of the Mittag-Leffler function under the Laplace transform. By using distributional representation, the Laplace transform of the Riemann zeta function is computed and applied in generalized fractional calculus, resulting in new images under various fractional transforms.

FRACTAL AND FRACTIONAL (2022)

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Article Multidisciplinary Sciences

A Survey of Some Recent Developments on Higher Transcendental Functions of Analytic Number Theory and Applied Mathematics

Hari Mohan Srivastava

Summary: This article provides an overview of the applications of higher transcendental functions in mathematical physics, analytic number theory, and applied mathematical sciences, while also summarizing recent theoretical developments and providing references for further reading and research. It also discusses operators of fractional calculus associated with higher transcendental functions and their applications.

SYMMETRY-BASEL (2021)

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Article Mathematics, Applied

A new representation of the extended k-gamma function with applications

Asifa Tassaddiq

Summary: This study investigates a new series representation of the extended k-gamma function, which proves useful for solving fractional kinetic equations. The new representation also helps compute new integrals and discuss distributional properties of the extended k-gamma function via Fourier transform.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES (2021)

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Article Mathematics, Applied