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

Sotiris K. Ntouyas

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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.

Mild solution of fractional order differential equations with not instantaneous impulses

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In this paper, we investigate the boundary value problems of fractional order differential equations with not instantaneous impulse. By some fixed-point theorems, the existence results of mild solution are established. At last, one example is also given to illustrate the results.

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

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

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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.

Boundary value problems for differential inclusions with fractional order

Mouffak Benchohra, Samira Hamani (2008)

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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.

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.

Positive solutions for higher-order nonlinear fractional differential equation with integral boundary condition.

Yang, Aijun, Wang, Helin (2011)

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An existence theorem for fractional hybrid differential inclusions of Hadamard type

Bashir Ahmad, Sotiris K. Ntouyas (2014)

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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.

Results for Mild solution of fractional coupled hybrid boundary value problems

Dumitru Baleanu, Hossein Jafari, Hasib Khan, Sarah Jane Johnston (2015)

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The study of coupled system of hybrid fractional differential equations (HFDEs) needs the attention of scientists for the exploration of its different important aspects. Our aim in this paper is to study the existence and uniqueness of mild solution (EUMS) of a coupled system of HFDEs. The novelty of this work is the study of a coupled system of fractional order hybrid boundary value problems (HBVP) with n initial and boundary hybrid conditions. For this purpose, we are utilizing some...

Nonlinear fractional differential inclusion with nonlocal fractional integro-differential boundary conditions in Banach spaces

Djamila Seba (2017)

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We consider a nonlinear fractional differential inclusion with nonlocal fractional integro-differential boundary conditions in a Banach space. The existence of at least one solution is proved by using the set-valued analog of Mönch fixed point theorem associated with the technique of measures of noncompactness.

Boundary value problems for differential equations with fractional order.

Benchohra, Mouffak, Hamani, Samira, Ntouyas, Sotiris K. (2008)

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

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

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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.

Positive solutions for a system of fractional boundary value problems

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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.

Solvability of nonlinear Langevin equation involving two fractional orders with Dirichlet boundary conditions.

Ahmad, Bashir, Nieto, Juan J. (2010)

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Existence of solutions of generalized fractional differential equation with nonlocal initial condition

Sandeep P. Bhairat, Dnyanoba-Bhaurao Dhaigude (2019)

Mathematica Bohemica

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This paper is devoted to studying the existence of solutions of a nonlocal initial value problem involving generalized Katugampola fractional derivative. By using fixed point theorems, the results are obtained in weighted space of continuous functions. Illustrative examples are also given.