• Title/Summary/Keyword: Fractional boundary value problem

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MULTIPLE POSITIVE SOLUTIONS OF NONLINEAR BOUNDARY VALUE PROBLEM WITH FINITE FRACTIONAL DIFFERENCE

  • He, Yansheng;Hou, Chengmin
    • Journal of the Chungcheong Mathematical Society
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    • v.28 no.2
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    • pp.173-186
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    • 2015
  • In this paper, we consider a discrete fractional nonlinear boundary value problem in which nonlinear term f is involved with the fractional order difference. We transform the fractional boundary value problem into boundary value problem of integer order difference equation. By using a generalization of Leggett-Williams fixed-point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of at least three positive solutions.

POSITIVE SOLUTIONS FOR MULTI-POINT BOUNDARY VALUE PROBLEM OF FRACTIONAL FUNCTIONAL DIFFERENTIAL EQUATIONS

  • Wang, Haihua
    • Journal of applied mathematics & informatics
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    • v.30 no.1_2
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    • pp.147-160
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    • 2012
  • In this paper, we establish some sufficient conditions for the existence of positive solutions for a class of multi-point boundary value problem for fractional functional differential equations involving the Caputo fractional derivative. Our results are based on two fixed point theorems. Two examples are also provided to illustrate our main results.

ANALYTIC SOLUTION OF HIGH ORDER FRACTIONAL BOUNDARY VALUE PROBLEMS

  • Muner M. Abou Hasan;Soliman A. Alkhatib
    • Nonlinear Functional Analysis and Applications
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    • v.28 no.3
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    • pp.601-612
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    • 2023
  • The existence of solution of the fractional order differential equations is very important mathematical field. Thus, in this work, we discuss, under some hypothesis, the existence of a positive solution for the nonlinear fourth order fractional boundary value problem which includes the p-Laplacian transform. The proposed method in the article is based on the fixed point theorem. More precisely, Krasnosilsky's theorem on a fixed point and some properties of the Green's function were used to study the existence of a solution for fourth order fractional boundary value problem. The main theoretical result of the paper is explained by example.

ANALYSIS OF SOLUTIONS FOR THE BOUNDARY VALUE PROBLEMS OF NONLINEAR FRACTIONAL INTEGRODIFFERENTIAL EQUATIONS INVOLVING GRONWALL'S INEQUALITY IN BANACH SPACES

  • KARTHIKEYAN, K.;RAJA, D. SENTHIL;SUNDARARAJAN, P.
    • Journal of applied mathematics & informatics
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    • v.40 no.1_2
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    • pp.305-316
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    • 2022
  • We study the existence and uniqueness of solutions for a class of boundary value problems of nonlinear fractional order differential equations involving the Caputo fractional derivative by employing the Banach's contraction principle and the Schauder's fixed point theorem. In addition, an example is given to demonstrate the application of our main results.

SOLVABILITY OF MULTI-POINT BOUNDARY VALUE PROBLEMS FOR FRACTIONAL DIFFERENTIAL EQUATIONS AT RESONANCE

  • Liu, Yuji;Liu, Xingyuan
    • Journal of the Chungcheong Mathematical Society
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    • v.25 no.3
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    • pp.425-443
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    • 2012
  • Sufficient conditions for the existence of at least one solution of a class of multi-point boundary value problems of the fractional differential equations at resonance are established. The main theorem generalizes and improves those ones in [Liu, B., Solvability of multi-point boundary value problems at resonance(II), Appl. Math. Comput., 136(2003)353-377], see Remark 2.3. An example is presented to illustrate the main results.

MULTIPLE POSITIVE SOLUTIONS OF INTEGRAL BOUNDARY VALUE PROBLEMS FOR FRACTIONAL DIFFERENTIAL EQUATIONS

  • Liu, Xiping;Jin, Jingfu;Jia, Mei
    • Journal of applied mathematics & informatics
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    • v.30 no.1_2
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    • pp.305-320
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    • 2012
  • In this paper, we study a class of integral boundary value problems for fractional differential equations. By using some fixed point theorems, the results of existence of at least three positive solutions for the boundary value problems are obtained.

Positive Solutions for Three-point Boundary Value Problem of Nonlinear Fractional q-difference Equation

  • Yang, Wengui
    • Kyungpook Mathematical Journal
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    • v.56 no.2
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    • pp.419-430
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    • 2016
  • In this paper, we investigate the existence and uniqueness of positive solutions for three-point boundary value problem of nonlinear fractional q-difference equation. Some existence and uniqueness results are obtained by applying some standard fixed point theorems. As applications, two examples are presented to illustrate the main results.

QUALITATIVE ANALYSIS OF ABR-FRACTIONAL VOLTERRA-FREDHOLM SYSTEM

  • Shakir M. Atshan;Ahmed A. Hamoud
    • Nonlinear Functional Analysis and Applications
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    • v.29 no.1
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    • pp.113-130
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    • 2024
  • In this work, we explore the existence and uniqueness results for a class of boundary value issues for implicit Volterra-Fredholm nonlinear integro-differential equations (IDEs) with Atangana-Baleanu-Riemann fractional (ABR-fractional) that have non-instantaneous multi-point fractional boundary conditions. The findings are supported by Krasnoselskii's fixed point theorem, Gronwall-Bellman inequality, and the Banach contraction principle. Finally, a demonstrative example is provided to support our key findings.

POSITIVE SOLUTIONS OF MULTI-POINT BOUNDARY VALUE PROBLEMS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION AT RESONANCE

  • Yang, Aijun;Ge, Weigao
    • The Pure and Applied Mathematics
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    • v.16 no.2
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    • pp.213-225
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    • 2009
  • This paper deals with the existence of positive solutions for a kind of multi-point nonlinear fractional differential boundary value problem at resonance. Our main approach is different from the ones existed and our main ingredient is the Leggett-Williams norm-type theorem for coincidences due to O'Regan and Zima. The most interesting point is the acquisition of positive solutions for fractional differential boundary value problem at resonance. And an example is constructed to show that our result here is valid.

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