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Bansal, Manish Kumar,Kumar, Devendra,Jain, Rashmi Department of Mathematics 2019 Kyungpook mathematical journal Vol.59 No.3
In this work, we evaluate the Mellin transform of the Marichev-Saigo-Maeda fractional integral operator with Appell's function $F_3$ type kernel. We then discuss six special cases of the result involving the Saigo fractional integral operator, the $Erd{\acute{e}}lyi$-Kober fractional integral operator, the Riemann-Liouville fractional integral operator and the Weyl fractional integral operator. We obtain new and known results as special cases of our main results. Finally, we obtain the images of S-generalized Gauss hypergeometric function under the operators of our study.
A GENERALIZATION OF THE KINETIC EQUATION USING THE PRABHAKAR-TYPE OPERATORS
( Gustavo Abel Dorrego ),( Dinesh Kumar ) 호남수학회 2017 호남수학학술지 Vol.39 No.3
Fractional kinetic equations are investigated in order to describe the various phenomena governed by anomalous reaction in dynamical systems with chaotic motion. Many authors have provided solutions of various families of fractional kinetic equations involving special functions. Here, in this paper, we aim at presenting solutions of certain general families of fractional kinetic equations using Prabhakar-type operators. The idea of present paper is motivated by Tomovski et al. [21].
SOME FAMILIES OF INFINITE SERIES SUMMABLE VIA FRACTIONAL CALCULUS OPERATORS
Tu, Shih-Tong,Wang, Pin-Yu,Srivastava, H.M. The Youngnam Mathematical Society Korea 2002 East Asian mathematical journal Vol.18 No.1
Many different families of infinite series were recently observed to be summable in closed forms by means of certain operators of fractional calculus(that is, calculus of integrals and derivatives of any arbitrary real or complex order). In this sequel to some of these recent investigations, the authors present yet another instance of applications of certain fractional calculus operators. Alternative derivations without using these fractional calculus operators are shown to lead naturally a family of analogous infinite sums involving hypergeometric functions.
A GENERALIZATION OF THE KINETIC EQUATION USING THE PRABHAKAR-TYPE OPERATORS
Dorrego, Gustavo Abel,Kumar, Dinesh The Honam Mathematical Society 2017 호남수학학술지 Vol.39 No.3
Fractional kinetic equations are investigated in order to describe the various phenomena governed by anomalous reaction in dynamical systems with chaotic motion. Many authors have provided solutions of various families of fractional kinetic equations involving special functions. Here, in this paper, we aim at presenting solutions of certain general families of fractional kinetic equations using Prabhakar-type operators. The idea of present paper is motivated by Tomovski et al. [21].
Jana, Ranjan Kumar,Pal, Ankit,Shukla, Ajay Kumar Korean Mathematical Society 2021 대한수학회논문집 Vol.36 No.1
This paper devoted to obtain some fractional integral properties of generalized Bessel function using pathway fractional integral operator. We also find the pathway transform of the generalized Bessel function in terms of Fox H-function.
Pathway fractional integral operator associated with struve function of first kind
K.S. NISAR,S.R. MONDAL,Praveen Agarwal 장전수학회 2016 Advanced Studies in Contemporary Mathematics Vol.26 No.1
The aim of this paper to study the pathway fractional integral operator as- sociated with the Struve function of rst kind which is expressed in terms of the general- izedWright hypergeometric function. Furthermore the special cases for the trigonometric functions are also consider.
Lee, S.K.,Khairnar, S.M.,More, Meena The Kangwon-Kyungki Mathematical Society 2009 한국수학논문집 Vol.17 No.2
In this paper we introduce a new subclass $K_{\mu}^{\lambda},{\phi},{\eta}(n;{\rho};{\alpha})$ of analytic and multivalent functions with negative coefficients using fractional calculus operators. Connections to the well known and some new subclasses are discussed. A necessary and sufficient condition for a function to be in $K_{\mu}^{\lambda},{\phi},{\eta}(n;{\rho};{\alpha})$ is obtained. Several distortion inequalities involving fractional integral and fractional derivative operators are also presented. We also give results for radius of starlikeness, convexity and close-to-convexity and inclusion property for functions in the subclass. Modified Hadamard product, application of class preserving integral operator and other interesting properties are also discussed.
THE (k, s)-FRACTIONAL CALCULUS OF CLASS OF A FUNCTION
Rahman, G.,Ghaffar, A.,Nisar, K.S.,Azeema, Azeema The Honam Mathematical Society 2018 호남수학학술지 Vol.40 No.1
In this present paper, we deal with the generalized (k, s)-fractional integral and differential operators recently defined by Nisar et al. and obtain some generalized (k, s)-fractional integral and differential formulas involving the class of a function as its kernels. Also, we investigate a certain number of their consequences containing the said function in their kernels.
S. P. Goyal,R. Mukherjee,R. Jain 경북대학교 자연과학대학 수학과 2004 Kyungpook mathematical journal Vol.44 No.4
In the present paper, we establish a general theorem exhibiting a relationship existing between the Laplace transform and the generalized Weyl fractional integral operator (FIO) of related functions. This theorem is very general in nature and involves a multidimensional series with essentially arbitrary sequence of complex numbers. By suitably assigning different values to these sequences, one can easily evaluate the generalized Weyl fractional integral operator of special functions of several variables. References of known results which follow as special cases of our theorem are also cited. We have obtained here as applications of the theorem, the generalized Weyl fractional integral of(Srivastava-Daoust) generalized Lauricella function which gives a number of results involving special functions of one or more variables merely by specializing the parameters. The results recently obtained by R. Jain and M. A. Pathan and S. P. Goyal and Ritu Goyal,etc. follow as special cases of our main findings.
SOME INTEGRAL TRANSFORMS AND FRACTIONAL INTEGRAL FORMULAS FOR THE EXTENDED HYPERGEOMETRIC FUNCTIONS
Agarwal, Praveen,Choi, Junesang,Kachhia, Krunal B.,Prajapati, Jyotindra C.,Zhou, Hui Korean Mathematical Society 2016 대한수학회논문집 Vol.31 No.3
Integral transforms and fractional integral formulas involving well-known special functions are interesting in themselves and play important roles in their diverse applications. A large number of integral transforms and fractional integral formulas have been established by many authors. In this paper, we aim at establishing some (presumably) new integral transforms and fractional integral formulas for the generalized hypergeometric type function which has recently been introduced by Luo et al. [9]. Some interesting special cases of our main results are also considered.