A new Riemann–Liouville type fractional derivative operator and its application in generating functions

Here, the concept of a new and interesting Riemann–Liouville type fractional derivative operator is exploited. Treatment of a fractional derivative operator has been made associated with the extended Appell hypergeometric functions of two variables and Lauricella hypergeometric function of three var...

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Published in:Advances in difference equations 2018-05, Vol.2018 (1), p.1-16, Article 167
Main Authors: Shadab, M., Khan, M. Faisal, Lopez-Bonilla, J. Luis
Format: Article
Language:English
Subjects:
Analysis
Difference and Functional Equations
Extended Appell functions
Extended beta function
Extended Lauricella function
Functional Analysis
Generating function
Hypergeometric functions
Mathematical analysis
Mathematics
Mathematics and Statistics
Mellin Transform
Mellin transforms
Operators (mathematics)
Ordinary Differential Equations
Partial Differential Equations
Riemann–Liouville fractional derivative operator
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creator Shadab, M.
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description Here, the concept of a new and interesting Riemann–Liouville type fractional derivative operator is exploited. Treatment of a fractional derivative operator has been made associated with the extended Appell hypergeometric functions of two variables and Lauricella hypergeometric function of three variables. With a view on analytic properties and application of new Riemann–Liouville type fractional derivative operator, we have obtained new fractional derivative formulas for some familiar functions and for Mellin transformation formulas. For the sake of justification of our new operator, we have established some presumably new generating functions for an extended hypergeometric function using the new definition of fractional derivative operator.
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subjects Analysis
Difference and Functional Equations
Extended Appell functions
Extended beta function
Extended Lauricella function
Functional Analysis
Generating function
Hypergeometric functions
Mathematical analysis
Mathematics
Mathematics and Statistics
Mellin Transform
Mellin transforms
Operators (mathematics)
Ordinary Differential Equations
Partial Differential Equations
Riemann–Liouville fractional derivative operator
title A new Riemann–Liouville type fractional derivative operator and its application in generating functions
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