Exploring multi-index functions with significance relations and associated with general properties in fractional calculus

Volume 34, Issue 2, pp 176--190 https://dx.doi.org/10.22436/jmcs.034.02.07

Publication Date: March 06, 2024 Submission Date: December 29, 2023 Revision Date: January 20, 2024 Accteptance Date: January 23, 2024

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Authors

R. S. Ali - Department of Mathematics, University of Lahore, Lahore, Pakistan. A. Liaqat - Department of Mathematics, University of Lahore, Lahore, Pakistan. Kh. W. N. Tajer - Department of Mathematics, College of Science and Arts, Qassim University, Ar Rass 51452, Saudi Arabia. R. M. Boshnak - Department of Mathematics, College of Science and Arts, Qassim University, Al-Mithnab 51951, Saudi Arabia. B. A. A. Yousif - Department of Mathematics, College of Science and Arts, Qassim University, Unayzah 51911, Saudi Arabia.

Abstract

The extensions and generalization of the special functions including in particular Pochhammer symbol, hypergeometric functions, Mittag-Leffler type functions, and Bessel-Maitland functions are the main core for the development of fractional operators by means of its kernel. We present a new extension of the multi-inde Mittag Leffler (MML) function and multi-index Bessel-Maitland (MBM) function by using the generalized Pochhammer symbol. Moreover, we establish some significance relations of such type of multi-index functions with other existing versions of Mittag-Leffler and Bessel-Maitland functions. Moreover, we analyze the behavior of some well-known fractional operators like as Saigo's fractional integral (SFI), Erdeyli fractional integral (EFI) and Riemann fractional integral (RFI) with the product of newly describe multi-index functions.

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Keywords

• Bessel-Maitland function
• fractional operators
• hypergeometric functions
• Mittag-Leffler function
• mathematical operators

MSC

•  33C10
•  26A33
•  33Cxx
•  33E12
•  45P05

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