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FRACTIONAL INTEGRAL OPERATORS INVOLVING GENERALIZED STRUVE FUNCTION
Kottakkaran Sooppy Nisar 장전수학회 2017 Proceedings of the Jangjeon mathematical society Vol.20 No.4
Fractional calculus has found many demonstrated applica- tions in extensive fields of engineering and applied science such as uid mechanics, biological population models, optics, signal processing and control theory.The effectiveness and application of the Struve function in various science problems,here,in this paper we propose to investigate fractional integral operators involving generalized Struve function.The obtained results is general in nature and it is useful to investigate many problems in applied mathematics.
Powers of generalized Bessel and Struve functions
Kottakkaran Sooppy Nisar,최준상,Saiful Rahman Mondal 장전수학회 2016 Advanced Studies in Contemporary Mathematics Vol.26 No.4
Baricz [2] used a very old formula due to L. Euler to present an alternative derivation of the MacLaurin series expansion of powers of the modified Bessel function Iv(x) of the first kind of order v. Motivated essentially by this work and using the Euler's formula, we also present the MacLaurin series expansions of powers of the generalized Bessel functions aIv (x) of the rst kind and the Struve functions Hv (x) of order v.
ON A CERTAIN EXTENSION OF THE RIEMANN-LIOUVILLE FRACTIONAL DERIVATIVE OPERATOR
Nisar, Kottakkaran Sooppy,Rahman, Gauhar,Tomovski, Zivorad Korean Mathematical Society 2019 대한수학회논문집 Vol.34 No.2
The main aim of this present paper is to present a new extension of the fractional derivative operator by using the extension of beta function recently defined by Shadab et al. [19]. Moreover, we establish some results related to the newly defined modified fractional derivative operator such as Mellin transform and relations to extended hypergeometric and Appell's function via generating functions.
Nisar, Kottakkaran Sooppy,Rahman, Gauhar,Choi, Junesang,Mubeen, Shahid,Arshad, Muhammad The Youngnam Mathematical Society 2018 East Asian mathematical journal Vol.34 No.3
We aim to establish certain Gronwall type inequalities associated with Riemann-Liouville k- and Hadamard k-fractional derivatives. The results presented here are sure to be new and potentially useful, in particular, in analyzing dependence solutions of certain k-fractional differential equations of arbitrary real order with initial conditions. Some interesting special cases of our main results are also considered.
ON THE GENERALIZED MODIFIED k-BESSEL FUNCTIONS OF THE FIRST KIND
Nisar, Kottakkaran Sooppy Korean Mathematical Society 2017 대한수학회논문집 Vol.32 No.4
The recent research investigates the generalization of Bessel function in different forms as its usefulness in various fields of applied sciences. In this paper, we introduce a new modified form of k-Bessel functions called the generalized modified k-Bessel functions and established some of its properties.
A novel kind of Hermite based Frobenius type Eulerian polynomials
Waseem Ahmad Khan,Kottakkaran Sooppy Nisar,MEHMET ACIKGOZ,UGUR DURAN 장전수학회 2019 Proceedings of the Jangjeon mathematical society Vol.22 No.4
After the inspirational innovation of fuzzy set by Zadeh in 1965, Kramosil and Michalek in 1975 pioneered the concept of fuzziness in metric spaces and very rst they formulated the notion of fuzzy met- ric spaces. Jungck introduced the idea of commutativity (in 1976) and compatibility (1986) in metric spaces and same are utilized by Subrah- manyam (in 1995) in fuzzy metric spaces to prove an analogues version of Jungck result. In this paper, we prove common xed point theorems for a pair of self-maps by introducing a new contraction which neither requires completeness of spaces nor continuity and compatible property of maps. An open problem and an example is given to justify the im- portance of our main result.
AN EXTENSION OF THE WHITTAKER FUNCTION
Choi, Junesang,Nisar, Kottakkaran Sooppy,Rahman, Gauhar Korean Mathematical Society 2021 대한수학회논문집 Vol.36 No.4
The Whittaker function and its diverse extensions have been actively investigated. Here we aim to introduce an extension of the Whittaker function by using the known extended confluent hypergeometric function 𝚽<sub>p,v</sub> and investigate some of its formulas such as integral representations, a transformation formula, Mellin transform, and a differential formula. Some special cases of our results are also considered.
Inequalities of extended $(p,q)$-beta and confluent hypergeometric functions
Shahid Mubeen,Kottakkaran Sooppy Nisar,Gauhar Rahman,Muhammad Arshad 호남수학회 2019 호남수학학술지 Vol.41 No.4
In this paper, we establish the log convexity and Tur\'{a}n type inequalities of extended $(p,q)$-beta functions. Likewise, we present the log-convexity, the monotonicity and Tur\'{a}n type inequalities for extended $(p,q)$-confluent hypergeometric function by utilizing the inequalities of extended $(p,q)$-beta functions.
INEQUALITIES OF EXTENDED (p, q)-BETA AND CONFLUENT HYPERGEOMETRIC FUNCTIONS
Mubeen, Shahid,Nisar, Kottakkaran Sooppy,Rahman, Gauhar,Arshad, Muhammad The Honam Mathematical Society 2019 호남수학학술지 Vol.41 No.4
In this paper, we establish the log convexity and Turán type inequalities of extended (p, q)-beta functions. Likewise, we present the log-convexity, the monotonicity and Turán type inequalities for extended (p, q)-confluent hypergeometric function by utilizing the inequalities of extended (p, q)-beta functions.
Pathway Fractional Integral Formulas Involving Extended Mittag-Leffler Functions in the Kernel
Rahman, Gauhar,Nisar, Kottakkaran Sooppy,Choi, Junesang,Mubeen, Shahid,Arshad, Muhammad Department of Mathematics 2019 Kyungpook mathematical journal Vol.59 No.1
Since the Mittag-Leffler function was introduced in 1903, a variety of extensions and generalizations with diverse applications have been presented and investigated. In this paper, we aim to introduce some presumably new and remarkably different extensions of the Mittag-Leffler function, and use these to present the pathway fractional integral formulas. We point out relevant connections of some particular cases of our main results with known results.