Displaying similar documents to “Infinitely many solutions for boundary value problems arising from the fractional advection dispersion equation”

Existence results for nonlocal boundary value problems for fractional differential equations and inclusions with fractional integral boundary conditions

Sotiris K. Ntouyas (2013)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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This paper studies a new class of nonlocal boundary value problems of nonlinear differential equations and inclusions of fractional order with fractional integral boundary conditions. Some new existence results are obtained by using standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also discussed.

Existence results for systems of conformable fractional differential equations

Bouharket Bendouma, Alberto Cabada, Ahmed Hammoudi (2019)

Archivum Mathematicum

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In this article, we study the existence of solutions to systems of conformable fractional differential equations with periodic boundary value or initial value conditions. where the right member of the system is L α 1 -carathéodory function. We employ the method of solution-tube and Schauder’s fixed-point theorem.

Multiplicity results for a class of fractional boundary value problems

Nemat Nyamoradi (2013)

Annales Polonici Mathematici

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We prove the existence of at least three solutions to the following fractional boundary value problem: ⎧ - d / d t ( 1 / 2 0 D t - σ ( u ' ( t ) ) + 1 / 2 t D T - σ ( u ' ( t ) ) ) - λ β ( t ) f ( u ( t ) ) - μ γ ( t ) g ( u ( t ) ) = 0 , a.e. t ∈ [0, T], ⎨ ⎩ u (0) = u (T) = 0, where 0 D t - σ and t D T - σ are the left and right Riemann-Liouville fractional integrals of order 0 ≤ σ < 1 respectively. The approach is based on a recent three critical points theorem of Ricceri [B. Ricceri, A further refinement of a three critical points theorem, Nonlinear Anal. 74 (2011), 7446-7454].

A Neighborhood Condition for Fractional ID-[A, B]-Factor-Critical Graphs

Sizhong Zhou, Fan Yang, Zhiren Sun (2016)

Discussiones Mathematicae Graph Theory

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Let G be a graph of order n, and let a and b be two integers with 1 ≤ a ≤ b. Let h : E(G) → [0, 1] be a function. If a ≤ ∑e∋x h(e) ≤ b holds for any x ∈ V (G), then we call G[Fh] a fractional [a, b]-factor of G with indicator function h, where Fh = {e ∈ E(G) : h(e) > 0}. A graph G is fractional independent-set-deletable [a, b]-factor-critical (in short, fractional ID-[a, b]- factor-critical) if G − I has a fractional [a, b]-factor for every independent set I of G. In this paper, it...

Anti-Periodic Boundary Value Problem for Impulsive Fractional Integro Differential Equations

Anguraj, A., Karthikeyan, P. (2010)

Fractional Calculus and Applied Analysis

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MSC 2010: 34A37, 34B15, 26A33, 34C25, 34K37 In this paper we prove the existence of solutions for fractional impulsive differential equations with antiperiodic boundary condition in Banach spaces. The results are obtained by using fractional calculus' techniques and the fixed point theorems.

Positive solutions for a system of fractional boundary value problems

Henderson, Johnny, Luca, Rodica

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We investigate the existence and multiplicity of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with nonnegative nonlinearities which can be nonsingular or singular functions, subject to multi-point boundary conditions that contain fractional derivatives.

Positive solutions for Hadamard differential systems with fractional integral conditions on an unbounded domain

Tariboon Jessada, Sotiris K. Ntouyas, Suphawat Asawasamrit, Chanon Promsakon (2017)

Open Mathematics

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In this paper, we investigate the existence of positive solutions for Hadamard type fractional differential system with coupled nonlocal fractional integral boundary conditions on an infinite domain. Our analysis relies on Guo-Krasnoselskii’s and Leggett-Williams fixed point theorems. The obtained results are well illustrated with the aid of examples.

An existence theorem for fractional hybrid differential inclusions of Hadamard type

Bashir Ahmad, Sotiris K. Ntouyas (2014)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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This paper studies the existence of solutions for fractional hybrid differential inclusions of Hadamard type by using a fixed point theorem due to Dhage. The main result is illustrated with the aid of an example.

Boundary value problems for differential inclusions with fractional order

Mouffak Benchohra, Samira Hamani (2008)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper, we shall establish sufficient conditions for the existence of solutions for a boundary value problem for fractional differential inclusions. Both cases of convex valued and nonconvex valued right hand sides are considered.

Multiplicity solutions of a class fractional Schrödinger equations

Li-Jiang Jia, Bin Ge, Ying-Xin Cui, Liang-Liang Sun (2017)

Open Mathematics

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In this paper, we study the existence of nontrivial solutions to a class fractional Schrödinger equations (−Δ)su+V(x)u=λf(x,u)inRN, ( - Δ ) s u + V ( x ) u = λ f ( x , u ) in ℝ N , where [...] (−Δ)su(x)=2limε→0∫RN∖Bε(X)u(x)−u(y)|x−y|N+2sdy,x∈RN ( - Δ ) s u ( x ) = 2 lim ε → 0 ∫ ℝ N ∖ B ε ( X ) u ( x ) - u ( y ) | x - y | N + 2 s d y , x ∈ ℝ N is a fractional operator and s ∈ (0, 1). By using variational methods, we prove this problem has at least two nontrivial solutions in a suitable weighted fractional Sobolev space.

Existence of positive solutions for a fractional boundary value problem with lower-order fractional derivative dependence on the half-line

Amina Boucenna, Toufik Moussaoui (2014)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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The aim of this paper is to study the existence of solutions to a boundary value problem associated to a nonlinear fractional differential equation where the nonlinear term depends on a fractional derivative of lower order posed on the half-line. An appropriate compactness criterion and suitable Banach spaces are used and so a fixed point theorem is applied to obtain fixed points which are solutions of our problem.