Displaying similar documents to “Fractional integro-differential inclusions with state-dependent delay”

Weighted fractional differential equations with infinite delay in Banach spaces

Qixiang Dong, Can Liu, Zhenbin Fan (2016)

Open Mathematics

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This paper is devoted to the study of fractional differential equations with Riemann-Liouville fractional derivatives and infinite delay in Banach spaces. The weighted delay is developed to deal with the case of non-zero initial value, which leads to the unboundedness of the solutions. Existence and uniqueness results are obtained based on the theory of measure of non-compactness, Schaude’s and Banach’s fixed point theorems. As auxiliary results, a fractional Gronwall type inequality...

Existence results for impulsive semilinear fractional differential inclusions with delay in Banach spaces

Hammouche Hadda, Guerbati Kaddour, Benchohra Mouffak, Abada Nadjat (2013)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper, we introduce a new concept of mild solution of some class of semilinear fractional differential inclusions of order 0 < α < 1. Also we establish an existence result when the multivalued function has convex values. The result is obtained upon the nonlinear alternative of Leray-Schauder type.

Nonlinear Implicit Hadamard’s Fractional Differential Equationswith Delay in Banach Space

Mouffak Benchohra, Soufyane Bouriah, Jamal E. Lazreg, Juan J. Nieto (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In this paper, we establish sufficient conditions for the existence of solutions for nonlinear Hadamard-type implicit fractional differential equations with finite delay. The proof of the main results is based on the measure of noncompactness and the Darbo’s and Mönch’s fixed point theorems. An example is included to show the applicability of our results.

Hybrid fractional integro-differential inclusions

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

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper we study an existence result for initial value problems for hybrid fractional integro-differential inclusions. A hybrid fixed point theorem for a sum of three operators due to Dhage is used. An example illustrating the obtained result is also presented.

Existence results for fractional integro-differential inclusions with state-dependent delay

Giovana Siracusa, Hernán R. Henríquez, Claudio Cuevas (2017)

Nonautonomous Dynamical Systems

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In this paper we are concerned with a class of abstract fractional integro-differential inclusions with infinite state-dependent delay. Our approach is based on the existence of a resolvent operator for the homogeneous equation.We establish the existence of mild solutions using both contractive maps and condensing maps. Finally, an application to the theory of heat conduction in materials with memory is given.

Impulsive Fractional Differential Inclusions Involving the Caputo Fractional Derivative

Ait Dads, E., Benchohra, M., Hamani, S. (2009)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classification: 26A33, 34A37. In this paper, we establish sufficient conditions for the existence of solutions for a class of initial value problem for impulsive fractional differential inclusions involving the Caputo fractional derivative. Both cases of convex and nonconvex valued right-hand side are considered. The topological structure of the set of solutions is also considered.

On a partial Hadamard fractional integral inclusion

Aurelian Cernea (2016)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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We study a class of nonconvex Hadamard fractional integral inclusions and we establish some Filippov type existence results.