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    A New Generalization of Pochhammer Symbol and Its Applications
    (Walter De Gruyter Gmbh, 2020) Sahin, Recep; Yagci, Oguz
    In this paper, we introduce a new generalization of the Pochhammer symbol by means of the generalization of extended gamma function (4). Using the generalization of Pochhammer symbol, we give a generalization of the extended hypergeometric functions one or several variables. Also, we obtain various integral representations, derivative formulas and certain properties of these functions.
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    Öğe
    Degenerate Pochhammer symbol, degenerate Sumudu transform, and degenerate hypergeometric function with applications
    (Hacettepe Univ, Fac Sci, 2021) Yagci, Oguz; Sahin, Recep
    In the paper, we first define a degenerate Pochhammer symbol by using the degenerate gamma function and investigate its properties. By using the degenerate Pochhammer symbol, we introduce and investigate a degenerate hypergeometric function. We also define a degenerate Sumudu transform and investigate its properties by using degenerate exponential function. Finally, we give certain the integral representations, derivative formulas, integral transforms, factional calculus applications, and generating functions of the degenerate hypergeometric function.
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    Fractional Calculus of the Extended Hypergeometric Function
    (Walter De Gruyter Gmbh, 2020) Sahin, Recep; Yagci, Oguz
    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..
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    SOLUTION OF FRACTIONAL KINETIC EQUATIONS INVOLVING GENERALIZED HURWITZ-LERCH ZETA FUNCTION USING SUMUDU TRANSFORM
    (Ankara Univ, Fac Sci, 2021) Yagci, Oguz; Sahin, Recep
    Fractional kinetic equations (FKEs) comprising a large array of special functions have been extensively and successfully applied in specification and solving many significant problems of astrophysics and physics. In this present work, our aim is to demonstrate solutions of (FKEs) of the generalized Hurwitz-Lerch Zeta function by applying the Sumudu transform. In addition to these, solutions of (FKEs) in special conditions of generalised Hurwitz-Lerch Zeta function have been derived.