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Fractional Calculus of Extended Wright Function with Beta Operator

Authors: Kumawat, Pramila; Choudhary, Sangeeta;

Fractional Calculus of Extended Wright Function with Beta Operator

Abstract

{"references": ["Shiri, B., & Baleanu, D. (2022). A general fractional pollution model for lakes. Communications on Applied Mathematics and Computation, 1-26.", "Shiri, B., Wu, G. C., & Baleanu, D. (2021). Terminal value problems for the nonlinear systems of fractional differential equations. Applied Numerical Mathematics, 170, 162-178.", "Gu, C. Y., Zheng, F. X., & Shiri, B. (2021). Mittag-Leffler stability analysis of tempered fractional neural networks with short memory and variable-order. Fractals, 29(08), 2140029.", "Gu, C. Y., Wu, G. C., & Shiri, B. (2021). An inverse problem approach to determine possible memory length of fractional differential equations. Fractional Calculus and Applied Analysis, 24(6), 1919-1936.", "Baleanu, D., Shiri, B., & Shiri, B. (2022). Nonlinear higher order fractional terminal value problems. AIMS Math, 7(5), 7489-7506.", "E. D. Rainville, Special Functions, The Macmillan Company, New York, USA,(1971).", "Wright, E. M. (1940). The asymptotic expansion of integral functions defined by Taylor series. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 238(795), 423-451", "Wright, E. M. (1935). The asymptotic expansion of the generalized hypergeometric function. Journal of the London Mathematical Society, 46, 389\u2013408.", "Wright, E. M. (1933). On the coefficients of power series having exponential singularities. Journal of the London Mathematical Society, 1(1), 71-79.", "Wright, E. M. (1935). The asymptotic expansion of the generalized hypergeometric function. Journal of the London Mathematical Society, 1(4), 286-293."]}

In this paper, Caputo Marichev-Saigo-Maeda (MSM) fractional operators of extended Wright function are discussed with beta operator. Some corollaries of our main results are also discussed. A beta operator is applied on the right-sided and left-sided MSM fractional operators with extended Wright function.

Keywords

Beta operator, caputo marichev-saigo-maeda operator, fractional differential and integral operator, extended wright function

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