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 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.

scholarly journals Existence of Solutions for Anti-Periodic Fractional Differential Inclusions with ψ-Caupto Fractional Derivative

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Dandan Yang ◽  
Chuanzhi Bai
Keyword(s):  
Fractional Derivative ◽  
Differential Inclusions ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Fractional Differential Inclusions ◽  
Fractional Differential ◽  
Special Case ◽  
Fractional Boundary Value Problems

In this paper, we investigate the existence of solutions for a class of fractional boundary value problems with anti-periodic boundary value conditions with ψ-Caupto fractional derivative. By means of some standard fixed point theorems, sufficient conditions for the existence of solutions for the fractional differential inclusions with ψ-Caputo derivatives are presented. Our result generalizes the known special case if ψx=x and single known results to the multi-valued ones.

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.

scholarly journals Existence results of nonlinear generalized proportional fractional differential inclusions via the diagonalization technique

2021 ◽  
Vol 6 (11) ◽  
pp. 12832-12844
Author(s):  
Mohamed I. Abbas ◽  
◽  
Snezhana Hristova ◽  
Keyword(s):  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Existence Results ◽  
Inclusion Problem ◽  
Fractional Differential Inclusions ◽  
New Class ◽  
Nonlinear Alternative ◽  
Fractional Differential ◽  
Infinite Intervals ◽  
The Right

<abstract><p>The present paper is concerned with the existence of solutions of a new class of nonlinear generalized proportional fractional differential inclusions with the right-hand side contains a Carathèodory-type multi-valued nonlinearity on infinite intervals. The investigation of the proposed inclusion problem relies on the multi-valued form of Leray-Schauder nonlinear alternative incorporated with the diagonalization technique. By specializing the parameters involved in the problem at hand, an illustrated example is proposed.</p></abstract>

scholarly journals Hilfer fractional differential inclusions with Erdélyi–Kober fractional integral boundary condition

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Adel Lachouri ◽  
Mohammed S. Abdo ◽  
Abdelouaheb Ardjouni ◽  
Bahaaeldin Abdalla ◽  
Thabet Abdeljawad
Keyword(s):  
Differential Inclusions ◽  
Fractional Integral ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Integral Boundary Conditions ◽  
Fractional Differential Inclusions ◽  
Hilfer Fractional Derivative ◽  
Integral Boundary ◽  
Fractional Differential ◽  
Theoretical Results

AbstractIn this article, we debate the existence of solutions for a nonlinear Hilfer fractional differential inclusion with nonlocal Erdélyi–Kober fractional integral boundary conditions (FIBC). Both cases of convex- and nonconvex-valued right-hand side are considered. Our obtained results are new in the framework of Hilfer fractional derivative and Erdélyi–Kober fractional integral with FIBC via the fixed point theorems (FPTs) for a set-valued analysis. Some pertinent examples demonstrating the effectiveness of the theoretical results are presented.

scholarly journals Existence Results for Impulsive Fractional Differential Inclusions with Two Different Caputo Fractional Derivatives

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Dongdong Gao ◽  
Jianli Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Inclusions ◽  
Fractional Derivatives ◽  
Existence Results ◽  
Fractional Differential Inclusions ◽  
Caputo Fractional Derivatives ◽  
Integral Boundary ◽  
Fractional Differential ◽  
New Criteria

In this paper, we study the impulsive fractional differential inclusions with two different Caputo fractional derivatives and nonlinear integral boundary value conditions. Under certain assumptions, new criteria to guarantee the impulsive fractional impulsive fractional differential inclusion has at least one solution are established by using Bohnenblust-Karlin’s fixed point theorem. Also, some previous results will be significantly improved.

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 On Caputo–Hadamard type coupled systems of nonconvex fractional differential inclusions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Samiha Belmor ◽  
Fahd Jarad ◽  
Thabet Abdeljawad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Coupled Systems ◽  
Fractional Differential Inclusions ◽  
Research Article ◽  
Fractional Differential

AbstractThis research article is mainly concerned with the existence of solutions for a coupled Caputo–Hadamard of nonconvex fractional differential inclusions equipped with boundary conditions. We derive our main result by applying Mizoguchi–Takahashi’s fixed point theorem with the help of $\mathcal{P}$ P -function characterizations.

scholarly journals Existence of Solutions for Fractional Differential Inclusions with Separated Boundary Conditions in Banach Space

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Mabrouk Bragdi ◽  
Amar Debbouche ◽  
Dumitru Baleanu
Keyword(s):  
Banach Space ◽  
Differential Inclusions ◽  
Existence Result ◽  
Existence Of Solutions ◽  
Necessary Conditions ◽  
Fractional Differential Inclusions ◽  
Separated Boundary Conditions ◽  
Fractional Differential ◽  
Fixed Point Technique ◽  
Fractional Orders

We discuss the existence of solutions for a class of some separated boundary differential inclusions of fractional orders2<α<3involving the Caputo derivative. In order to obtain necessary conditions for the existence result, we apply the fixed point technique, fractional calculus, and multivalued analysis.

scholarly journals Existence Results for Sequential Riemann–Liouville and Caputo Fractional Differential Inclusions with Generalized Fractional Integral Conditions

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 1044
Author(s):  
Jessada Tariboon ◽  
Sotiris K. Ntouyas ◽  
Bashir Ahmad ◽  
Ahmed Alsaedi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Fractional Integral ◽  
Existence Results ◽  
Fractional Differential Inclusions ◽  
Integral Boundary ◽  
Generalized Fractional Integral ◽  
Fractional Differential

Under different criteria, we prove the existence of solutions for sequential fractional differential inclusions containing Riemann–Liouville and Caputo type derivatives and supplemented with generalized fractional integral boundary conditions. Our existence results rely on the endpoint theory, the Krasnosel’skiĭ’s fixed point theorem for multivalued maps and Wegrzyk’s fixed point theorem for generalized contractions. We demonstrate the application of the obtained results with the help of examples.

Sign in / Sign up

Export Citation Format

Share Document