Extended Conformable K-Hypergeometric Function and Its Application

The extended conformable k-hypergeometric function finds various applications in physics due to its ability to describe complex mathematical relationships arising in different physical scenarios. Here are a few instances of its uses in physics, including nuclear physics, fluid dynamics, quantum mech...

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Bibliographic Details
Published in:Advances in mathematical physics 2024-03, Vol.2024, p.1-12
Main Authors: Abdul Qayyum, Maham, Dhiaa, Aya Mohammed, Mahboob, Abid, Rasheed, Muhammad Waheed, Alameri, Abdu
Format: Article
Language:English
Subjects:
Applied mathematics
Astronomy
Calculus
Derivatives
Engineering
Fluid dynamics
Hypergeometric functions
Integrals
Mathematical analysis
Mathematical functions
Mellin transforms
Nuclear physics
Operators (mathematics)
Physics
Quantum mechanics
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Summary:The extended conformable k-hypergeometric function finds various applications in physics due to its ability to describe complex mathematical relationships arising in different physical scenarios. Here are a few instances of its uses in physics, including nuclear physics, fluid dynamics, quantum mechanics, and astronomy. The main objectives of this paper are to introduce the extended conformable k-hypergeometric and confluent hypergeometric functions by utilizing the new definition of the α,k-beta function and studying its important properties, like integral representation, summation formula, derivative formula, transform formula, and generating function. Also, introduce the extension of the Riemann–Liouville fractional derivative and establish some results related to the newly defined fractional operator, such as the Mellin transform and relations to extended α,k-hypergeometric functions.
ISSN:1687-9120
1687-9139
DOI:10.1155/2024/5709319