• Title/Summary/Keyword: Fractional operator

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CERTAIN FRACTIONAL INTEGRAL INEQUALITIES INVOLVING HYPERGEOMETRIC OPERATORS

  • Choi, Junesang;Agarwal, Praveen
    • East Asian mathematical journal
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    • v.30 no.3
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    • pp.283-291
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    • 2014
  • A remarkably large number of inequalities involving the fractional integral operators have been investigated in the literature by many authors. Very recently, Baleanu et al. [2] gave certain interesting fractional integral inequalities involving the Gauss hypergeometric functions. Using the same fractional integral operator, in this paper, we present some (presumably) new fractional integral inequalities whose special cases are shown to yield corresponding inequalities associated with Saigo, Erd$\acute{e}$lyi-Kober and Riemann-Liouville type fractional integral operators. Relevant connections of the results presented here with those earlier ones are also pointed out.

CERTAIN NEW PATHWAY TYPE FRACTIONAL INTEGRAL INEQUALITIES

  • Choi, Junesang;Agarwal, Praveen
    • Honam Mathematical Journal
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    • v.36 no.2
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    • pp.455-465
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    • 2014
  • In recent years, diverse inequalities involving a variety of fractional integral operators have been developed by many authors. In this sequel, here, we aim at establishing certain new inequalities involving pathway type fractional integral operator by following the same lines, recently, used by Choi and Agarwal [7]. Relevant connections of the results presented here with those earlier ones are also pointed out.

A Study of Marichev-Saigo-Maeda Fractional Integral Operators Associated with the S-Generalized Gauss Hypergeometric Function

  • Bansal, Manish Kumar;Kumar, Devendra;Jain, Rashmi
    • Kyungpook Mathematical Journal
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    • v.59 no.3
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    • pp.433-443
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    • 2019
  • 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.

WEAK FACTORIZATIONS OF H1 (ℝn) IN TERMS OF MULTILINEAR FRACTIONAL INTEGRAL OPERATOR ON VARIABLE LEBESGUE SPACES

  • Zongguang Liu;Huan Zhao
    • Bulletin of the Korean Mathematical Society
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    • v.60 no.6
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    • pp.1439-1451
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    • 2023
  • This paper provides a constructive proof of the weak factorizations of the classical Hardy space H1(ℝn) in terms of multilinear fractional integral operator on the variable Lebesgue spaces, which the result is new even in the linear case. As a direct application, we obtain a new proof of the characterization of BMO(ℝn) via the boundedness of commutators of the multilinear fractional integral operator on the variable Lebesgue spaces.

OPERATOR FRACTIONAL BROWNIAN SHEET AND MARTINGALE DIFFERENCES

  • Dai, Hongshuai;Shen, Guangjun;Xia, Liangwen
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.1
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    • pp.9-23
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    • 2018
  • In this paper, inspired by the fractional Brownian sheet of Riemann-Liouville type, we introduce the operator fractional Brownian sheet of Riemman-Liouville type, and study some properties of it. We also present an approximation in law to it based on the martingale differences.

CERTAIN FRACTIONAL INTEGRAL INEQUALITIES ASSOCIATED WITH PATHWAY FRACTIONAL INTEGRAL OPERATORS

  • Agarwal, Praveen;Choi, Junesang
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.1
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    • pp.181-193
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    • 2016
  • During the past two decades or so, fractional integral inequalities have proved to be one of the most powerful and far-reaching tools for the development of many branches of pure and applied mathematics. Very recently, many authors have presented some generalized inequalities involving the fractional integral operators. Here, using the pathway fractional integral operator, we give some presumably new and potentially useful fractional integral inequalities whose special cases are shown to yield corresponding inequalities associated with Riemann-Liouville type fractional integral operators. Relevant connections of the results presented here with those earlier ones are also pointed out.

ON A CERTAIN EXTENSION OF THE RIEMANN-LIOUVILLE FRACTIONAL DERIVATIVE OPERATOR

  • Nisar, Kottakkaran Sooppy;Rahman, Gauhar;Tomovski, Zivorad
    • Communications of the Korean Mathematical Society
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    • v.34 no.2
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    • pp.507-522
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    • 2019
  • 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.