Article
Fractional Calculus of the Extended Hypergeometric Function
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Abstract
Here, our aim is to demonstrate some formulae of generalization of the extended hypergeometric function by applying fractional derivative operators. Furthermore, by applying certain integral transforms on the resulting formulas and develop a new futher generalized form of the fractional kinetic equation involving the generalized Gauss hypergeometric function. Also, we obtain generating functions for generalization of extended hypergeometric function..
Keywords
Gamma function, beta function, hypergeometric functions, extended hypergeometric function, integral transforms, fractional calculus operators, generating functions, Primary 33C15, 33C20, 33C60, 33D70, Secondary 26A33, 33C65, 33C90
Citation
Şahin, R. & Yağcı, O. (2020). Fractional calculus of the extended hypergeometric function. Applied Mathematics and Nonlinear Sciences, 5(1), 369–384. https://doi.org/10.2478/amns.2020.1.00035
R. Şahin and O. Yağcı, “Fractional calculus of the extended hypergeometric function,” Applied Mathematics and Nonlinear Sciences, vol. 5, no. 1, pp. 369–384, 2020, doi: 10.2478/amns.2020.1.00035.
Şahin R, Yağcı O. Fractional calculus of the extended hypergeometric function. Applied Mathematics and Nonlinear Sciences. 2020;5(1):369–384. doi:10.2478/amns.2020.1.00035.
Şahin, R. and Yağcı, O. (2020), ‘Fractional calculus of the extended hypergeometric function’, Applied Mathematics and Nonlinear Sciences, 5(1), pp. 369–384. Available at: https://doi.org/10.2478/amns.2020.1.00035.
Şahin, Recep, and Oğuz Yağcı. “Fractional Calculus of the Extended Hypergeometric Function.” Applied Mathematics and Nonlinear Sciences, vol. 5, no. 1, 2020, pp. 369–384. https://doi.org/10.2478/amns.2020.1.00035.
Şahin, Recep, and Oğuz Yağcı. “Fractional Calculus of the Extended Hypergeometric Function.” Applied Mathematics and Nonlinear Sciences 5, no. 1 (2020): 369–384. https://doi.org/10.2478/amns.2020.1.00035.
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Published by: Engineering Journals


