• 제목/요약/키워드: Fractional Function

검색결과 327건 처리시간 0.026초

ON FRACTIONAL PROGRAMMING CONTAINING SUPPORT FUNCTIONS

  • HUSAIN I.;JABEEN Z.
    • Journal of applied mathematics & informatics
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    • 제18권1_2호
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    • pp.361-376
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    • 2005
  • Optimality conditions are derived for a nonlinear fractional program in which a support function appears in the numerator and denominator of the objective function as well as in each constraint function. As an application of these optimality conditions, a dual to this program is formulated and various duality results are established under generalized convexity. Several known results are deduced as special cases.

FRACTIONAL CALCULUS AND INTEGRAL TRANSFORMS OF INCOMPLETE τ-HYPERGEOMETRIC FUNCTION

  • Pandey, Neelam;Patel, Jai Prakash
    • 대한수학회논문집
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    • 제33권1호
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    • pp.127-142
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    • 2018
  • In the present article, authors obtained certain fractional derivative and integral formulas involving incomplete ${\tau}$-hypergeometric function introduced by Parmar and Saxena [14]. Some interesting special cases and consequences of our main results are also considered.

SOME SEQUENCE SPACES OVER n-NORMED SPACES DEFINED BY FRACTIONAL DIFFERENCE OPERATOR AND MUSIELAK-ORLICZ FUNCTION

  • Mursaleen, M.;Sharma, Sunil K.;Qamaruddin, Qamaruddin
    • Korean Journal of Mathematics
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    • 제29권2호
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    • pp.211-225
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    • 2021
  • In the present paper we introduce some sequence spaces over n-normed spaces defined by fractional difference operator and Musielak-Orlicz function 𝓜 = (𝕱i). We also study some topological properties and prove some inclusion relations between these spaces.

A NEW EXTENSION OF THE MITTAG-LEFFLER FUNCTION

  • Arshad, Muhammad;Choi, Junesang;Mubeen, Shahid;Nisar, Kottakkaran Sooppy;Rahman, Gauhar
    • 대한수학회논문집
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    • 제33권2호
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    • pp.549-560
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    • 2018
  • Since Mittag-Leffler introduced the so-called Mittag-Leffler function in 1903, due to its usefulness and diverse applications, a variety and large number of its extensions (and generalizations) and variants have been presented and investigated. In this sequel, we aim to introduce a new extension of the Mittag-Leffler function by using a known extended beta function. Then we investigate ceratin useful properties and formulas associated with the extended Mittag-Leffler function such as integral representation, Mellin transform, recurrence relation, and derivative formulas. We also introduce an extended Riemann-Liouville fractional derivative to present a fractional derivative formula for a known extended Mittag-Leffler function, the result of which is expressed in terms of the new extended Mittag-Leffler functions.

THE FUNDAMENTAL SOLUTION OF THE SPACE-TIME FRACTIONAL ADVECTION-DISPERSION EQUATION

  • HUANG F.;LIU F.
    • Journal of applied mathematics & informatics
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    • 제18권1_2호
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    • pp.339-350
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    • 2005
  • A space-time fractional advection-dispersion equation (ADE) is a generalization of the classical ADE in which the first-order time derivative is replaced with Caputo derivative of order $\alpha{\in}(0,1]$, and the second-order space derivative is replaced with a Riesz-Feller derivative of order $\beta{\in}0,2]$. We derive the solution of its Cauchy problem in terms of the Green functions and the representations of the Green function by applying its Fourier-Laplace transforms. The Green function also can be interpreted as a spatial probability density function (pdf) evolving in time. We do the same on another kind of space-time fractional advection-dispersion equation whose space and time derivatives both replacing with Caputo derivatives.

Certain Inequalities Involving Pathway Fractional Integral Operators

  • Choi, Junesang;Agarwal, Praveen
    • Kyungpook Mathematical Journal
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    • 제56권4호
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    • pp.1161-1168
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    • 2016
  • Belarbi and Dahmani [3], recently, using the Riemann-Liouville fractional integral, presented some interesting integral inequalities for the Chebyshev functional in the case of two synchronous functions. Subsequently, Dahmani et al. [5] and Sulaiman [17], provided some fractional integral inequalities. Here, motivated essentially by Belarbi and Dahmani's work [3], we aim at establishing certain (presumably) new inequalities associated with pathway fractional integral operators by using synchronous functions which are involved in the Chebychev functional. Relevant connections of the results presented here with those involving Riemann-Liouville fractional integrals are also pointed out.

EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR A SINGULAR SYSTEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH INTEGRAL BOUNDARY CONDITIONS

  • Wang, Lin;Lu, Xinyi
    • Journal of applied mathematics & informatics
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    • 제31권5_6호
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    • pp.877-894
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    • 2013
  • In this paper, we study the existence and uniqueness of solutions for a singular system of nonlinear fractional differential equations with integral boundary conditions. We obtain existence and uniqueness results of solutions by using the properties of the Green's function, a nonlinear alternative of Leray-Schauder type, Guo-Krasnoselskii's fixed point theorem in a cone. Some examples are included to show the applicability of our results.

SOME APPLICATIONS FOR GENERALIZED FRACTIONAL OPERATORS IN ANALYTIC FUNCTIONS SPACES

  • Kilicman, Adem;Abdulnaby, Zainab E.
    • Korean Journal of Mathematics
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    • 제27권3호
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    • pp.581-594
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    • 2019
  • In this study a new generalization for operators of two parameters type of fractional in the unit disk is proposed. The fractional operators in this generalization are in the Srivastava-Owa sense. Concerning with the related applications, the generalized Gauss hypergeometric function is introduced. Further, some boundedness properties on Bloch space are also discussed.

RIEMANN-LIOUVILLE FRACTIONAL VERSIONS OF HADAMARD INEQUALITY FOR STRONGLY (α, m)-CONVEX FUNCTIONS

  • Farid, Ghulam;Akbar, Saira Bano;Rathour, Laxmi;Mishra, Lakshmi Narayan
    • Korean Journal of Mathematics
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    • 제29권4호
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    • pp.687-704
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    • 2021
  • The refinement of an inequality provides better convergence of one quantity towards the other one. We have established the refinements of Hadamard inequalities for Riemann-Liouville fractional integrals via strongly (α, m)-convex functions. In particular, we obtain two refinements of the classical Hadamard inequality. By using some known integral identities we also give refinements of error bounds of some fractional Hadamard inequalities.