scholarly journals On Higher-Order Sequential Fractional Differential Inclusions with Nonlocal Three-Point Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris K. Ntouyas
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Differential Inclusions ◽  
Fixed Point Theorems ◽  
Existence Results ◽  
Point Boundary ◽  
Fractional Differential Inclusions ◽  
Multivalued Maps ◽  
Fractional Differential

We study a nonlinear three-point boundary value problem of sequential fractional differential inclusions of orderξ+1withn-1<ξ≤n,n≥2. Some new existence results for convex as well as nonconvex multivalued maps are obtained by using standard fixed point theorems. The paper concludes with an example.

Impulsive fractional differential inclusions with flux boundary conditions

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 953-961
Author(s):  
Hilmi Ergören
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Differential Inclusions ◽  
Existence Results ◽  
Fractional Differential Inclusions ◽  
Multivalued Maps ◽  
Flux Boundary Conditions ◽  
Fractional Differential

In this work we investigate some existence results for solutions of a boundary value problem for impulsive fractional differential inclusions supplemented with fractional flux boundary conditions by applying Bohnenblust-Karlin?s fixed point theorem for multivalued maps.

Existence of solutions for Riemann–Liouville multi-valued fractional boundary value problems

2017 ◽  
Vol 24 (4) ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris K. Ntouyas
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Differential Inclusions ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Existence Results ◽  
Fractional Differential Inclusions ◽  
Fractional Differential ◽  
Fractional Boundary Conditions ◽  
Fractional Boundary Value Problems

AbstractIn this paper, we study a class of Riemann–Liouville fractional differential inclusions with fractional boundary conditions. By using standard fixed point theorems, we obtain some new existence results for convex as well as nonconvex multi-valued mappings in an appropriate Banach space. The obtained results are illustrated by examples.

scholarly journals Compression–Expansion Fixed Point Theorems for Decomposable Maps and Applications to Discontinuous $$\phi $$-Laplacian problems

2021 ◽  
Vol 20 (3) ◽  
Author(s):  
Jorge Rodríguez–López
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Boundary Conditions ◽  
Fixed Point Theorems ◽  
Classical Case ◽  
Existence Results ◽  
Point Boundary ◽  
Discontinuous Nonlinearity ◽  
Multivalued Maps ◽  
Upper Semicontinuous

AbstractIn this paper, we prove new compression–expansion type fixed point theorems in cones for the so-called decomposable maps, that is, compositions of two upper semicontinuous multivalued maps. As an application, we obtain existence and localization of positive solutions for a differential equation with $$\phi $$ ϕ -Laplacian and discontinuous nonlinearity subject to multi-point boundary conditions. As far as we are aware, the existence results are new even in the classical case of continuous nonlinearities.

scholarly journals Existence results for a nonlinear fractional differential inclusion

Filomat ◽  
2021 ◽  
Vol 35 (3) ◽  
pp. 927-939
Author(s):  
Habib Djourdem
Keyword(s):  
Fixed Point ◽  
Differential Inclusions ◽  
Existence Results ◽  
Convex Compact ◽  
Fractional Differential Inclusions ◽  
Multivalued Maps ◽  
Nonlinear Alternative ◽  
Fractional Differential ◽  
The Right ◽  
Multivalued Contractions

In this paper, we establish some existence results for higher-order nonlinear fractional differential inclusions with multi-strip conditions, when the right-hand side is convex-compact as well as nonconvexcompact values. First, we use the nonlinear alternative of Leray-Schauder type for multivalued maps. We investigate the next result by using the well-known Covitz and Nadler?s fixed point theorem for multivalued contractions. The results are illustrated by two examples.

scholarly journals Application of fixed point theorems for multivalued maps to anti-periodic problems of fractional differential inclusions

Filomat ◽  
2014 ◽  
Vol 28 (1) ◽  
pp. 91-98
Author(s):  
Hamed Alsulami
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Inclusions ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Fractional Differential Inclusions ◽  
Multivalued Maps ◽  
Topological Dimension ◽  
Periodic Problems ◽  
Fractional Differential

This paper deals with the existence and dimension of the solution set for an anti-periodic boundary value problem of fractional differential inclusions. Our results rely on Wegrzyk?s fixed point theorem and a result on the topological dimension of the set of fixed points for multivalued maps.

scholarly journals Existence Results for Fractional Differential Inclusions with Multivalued Term Depending on Lower-Order Derivative

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Xiaoyou Liu ◽  
Zhenhai Liu
Keyword(s):  
Boundary Conditions ◽  
Lower Order ◽  
Differential Inclusions ◽  
Integral Boundary Conditions ◽  
Existence Results ◽  
Inclusion Problem ◽  
Fractional Differential Inclusions ◽  
Integral Boundary ◽  
Separated Boundary Conditions ◽  
Fractional Differential

This paper is concerned with a class of fractional differential inclusions whose multivalued term depends on lower-order fractional derivative with fractional (non)separated boundary conditions. The cases of convex-valued and non-convex-valued right-hand sides are considered. Some existence results are obtained by using standard fixed point theorems. A possible generalization for the inclusion problem with integral boundary conditions is also discussed. Examples are given to illustrate the results.

scholarly journals Existence results for fractional differential inclusions with Erdélyi-Kober fractional integral conditions

2017 ◽  
Vol 25 (2) ◽  
pp. 5-24 ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris K. Ntouyas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Fractional Integral ◽  
Existence Of Solutions ◽  
Existence Results ◽  
Fractional Differential Inclusions ◽  
Integral Conditions ◽  
Fractional Differential

Abstract In this paper, we discus the existence of solutions for Riemann- Liouville fractional differential inclusions supplemented with Erdélyi- Kober fractional integral conditions. We apply endpoint theory, Krasnoselskii’s multi-valued fixed point theorem and Wegrzyk's fixed point theorem for generalized contractions. For the illustration of our results, we include examples.

On a fractional differential inclusion with “maxima”

2016 ◽  
Vol 19 (5) ◽  
Author(s):  
Aurelian Cernea
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Differential Inclusion ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Existence Results ◽  
Fractional Differential Inclusion ◽  
Right Hand ◽  
Fractional Differential ◽  
The Right

Abstract We study a boundary value problem associated to a fractional differential inclusion with “maxima”. Several existence results are obtained by using suitable fixed point theorems when the right hand side has convex or non convex values.

scholarly journals Existence Results for Langevin Fractional Differential Inclusions Involving Two Fractional Orders with Four-Point Multiterm Fractional Integral Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
Ahmed Alsaedi ◽  
Sotiris K. Ntouyas ◽  
Bashir Ahmad
Keyword(s):  
Boundary Conditions ◽  
Differential Inclusions ◽  
Fractional Integral ◽  
Fixed Point Theorems ◽  
Integral Boundary Conditions ◽  
Fractional Differential Inclusions ◽  
Integral Boundary ◽  
Fractional Differential ◽  
The Right ◽  
Fractional Orders

We discuss the existence of solutions for Langevin fractional differential inclusions involving two fractional orders with four-point multiterm fractional integral boundary conditions. Our study relies on standard fixed point theorems for multivalued maps and covers the cases when the right-hand side of the inclusion has convex as well as nonconvex values. Illustrative examples are also presented.

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