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A study of second order differential inclusions with four-point integral boundary conditions

100%
Ahmad B., Ntouyas S.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2011
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tom 31
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nr 2
137-156
EN
In this paper, we discuss the existence of solutions for a four-point integral boundary value problem of second order differential inclusions involving convex and non-convex multivalued maps. The existence results are obtained by applying the nonlinear alternative of Leray Schauder type and some suitable theorems of fixed point theory.
2
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Nonlinear fractional differential inclusions with anti-periodic type integral boundary conditions

100%
Ahmad B., Ntouyas S.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2012
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tom 32
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nr 1
45-62
EN
This article studies a boundary value problem of nonlinear fractional differential inclusions with anti-periodic type integral boundary conditions. Some existence results are obtained via fixed point theorems. The cases of convex-valued and nonconvex-valued right hand sides are considered. Several new results appear as a special case of the results of this paper.
3
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An existence theorem for fractional hybrid differential inclusions of Hadamard type

100%
Ahmad B., Ntouyas S.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2014
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tom 34
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nr 2
207-218
EN
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.
4
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Existence theory for sequential fractional differential equations with anti-periodic type boundary conditions

81%
Aqlan M. H., Alsaedi A., Ahmad B., Nieto J. J.
Open Mathematics
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2016
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tom 14
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nr 1
723-735
EN
We develop the existence theory for sequential fractional differential equations involving Liouville-Caputo fractional derivative equipped with anti-periodic type (non-separated) and nonlocal integral boundary conditions. Several existence criteria depending on the nonlinearity involved in the problems are presented by means of a variety of tools of the fixed point theory. The applicability of the results is shown with the aid of examples. Our results are not only new in the given configuration but also yield some new special cases for specific choices of parameters involved in the problems.
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