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Displaying similar documents to “Positive solutions for a system of fractional boundary value problems”

System of fractional differential equations with Erdélyi-Kober fractional integral conditions

Natthaphong Thongsalee, Sorasak Laoprasittichok, Sotiris K. Ntouyas, Jessada Tariboon (2015)

Open Mathematics

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In this paper we study existence and uniqueness of solutions for a system consisting from fractional differential equations of Riemann-Liouville type subject to nonlocal Erdélyi-Kober fractional integral conditions. The existence and uniqueness of solutions is established by Banach’s contraction principle, while the existence of solutions is derived by using Leray-Schauder’s alternative. Examples illustrating our results are also presented.

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.

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.

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.

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.

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.

Fractional Derivatives in Spaces of Generalized Functions

Stojanović, Mirjana (2011)

Fractional Calculus and Applied Analysis

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MSC 2010: 26A33, 46Fxx, 58C05 Dedicated to 80-th birthday of Prof. Rudolf Gorenflo We generalize the two forms of the fractional derivatives (in Riemann-Liouville and Caputo sense) to spaces of generalized functions using appropriate techniques such as the multiplication of absolutely continuous function by the Heaviside function, and the analytical continuation. As an application, we give the two forms of the fractional derivatives of discontinuous functions in spaces of...

The general solution of impulsive systems with Riemann-Liouville fractional derivatives

Xianmin Zhang, Wenbin Ding, Hui Peng, Zuohua Liu, Tong Shu (2016)

Open Mathematics

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In this paper, we study a kind of fractional differential system with impulsive effect and find the formula of general solution for the impulsive fractional-order system by analysis of the limit case (as impulse tends to zero). The obtained result shows that the deviation caused by impulses for fractional-order system is undetermined. An example is also provided to illustrate the result.

Time fractional Kupershmidt equation: symmetry analysis and explicit series solution with convergence analysis

Astha Chauhan, Rajan Arora (2019)

Communications in Mathematics

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In this work, the fractional Lie symmetry method is applied for symmetry analysis of time fractional Kupershmidt equation. Using the Lie symmetry method, the symmetry generators for time fractional Kupershmidt equation are obtained with Riemann-Liouville fractional derivative. With the help of symmetry generators, the fractional partial differential equation is reduced into the fractional ordinary differential equation using Erdélyi-Kober fractional differential operator. The conservation...

Fractional derivative generalization of Noether’s theorem

Maryam Khorshidi, Mehdi Nadjafikhah, Hossein Jafari (2015)

Open Mathematics

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The symmetry of the Bagley–Torvik equation is investigated by using the Lie group analysis method. The Bagley–Torvik equation in the sense of the Riemann–Liouville derivatives is considered. Then we prove a Noetherlike theorem for fractional Lagrangian densities with the Riemann-Liouville fractional derivative and few examples are presented as an application of the theory.