scholarly journals Investigation of the neutral fractional differential inclusions of Katugampola-type involving both retarded and advanced arguments via Kuratowski MNC technique

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sina Etemad ◽  
Mohammed Said Souid ◽  
Benoumran Telli ◽  
Mohammed K. A. Kaabar ◽  
Shahram Rezapour
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Measure Of Noncompactness ◽  
Research Work ◽  
Neutral System ◽  
Fractional Differential Inclusions ◽  
Kuratowski Measure Of Noncompactness ◽  
Fractional Differential

AbstractA class of the boundary value problem is investigated in this research work to prove the existence of solutions for the neutral fractional differential inclusions of Katugampola fractional derivative which involves retarded and advanced arguments. New results are obtained in this paper based on the Kuratowski measure of noncompactness for the suggested inclusion neutral system for the first time. On the one hand, this research concerns the set-valued analogue of Mönch fixed point theorem combined with the measure of noncompactness technique in which the right-hand side is convex valued. On the other hand, the nonconvex case is discussed via Covitz and Nadler fixed point theorem. An illustrative example is provided to apply and validate our obtained 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.

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 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.

scholarly journals A fixed point theorem for generalized contractive type set-valued mappings with application to nonlinear fractional differential inclusions

Filomat ◽  
2018 ◽  
Vol 32 (15) ◽  
pp. 5361-5370
Author(s):  
Zeinab Soltani
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Inclusion ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Existence Of Solution ◽  
Fractional Differential Inclusions ◽  
Contractive Type ◽  
Fractional Differential ◽  
Set Valued Mappings

In this paper, we present some fixed point results for set-valued mappings of contractive type by using the concept of ?-distance. As an application, we prove the existence of solution of nonlinear fractional differential inclusion.

scholarly journals Ulam Stabilities for the Darboux Problem for Partial Fractional Differential Inclusions

2014 ◽  
Vol 47 (4) ◽  
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Fractional Differential Inclusions ◽  
Darboux Problem ◽  
Gronwall’S Inequality ◽  
Fractional Differential ◽  
Ulam’S Type Stability ◽  
Stability Concepts

AbstractIn this article, we investigate some Ulam’s type stability concepts for the Darboux problem of partial fractional differential inclusions with a nonconvex valued right hand side. Our results are based upon Covitz-Nadler fixed point theorem and fractional version of Gronwall’s inequality.

scholarly journals Exact Controllability for Hilfer Fractional Differential Inclusions Involving Nonlocal Initial Conditions

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Jun Du ◽  
Wei Jiang ◽  
Denghao Pang ◽  
Azmat Ullah Khan Niazi
Keyword(s):  
Fixed Point ◽  
Differential Inclusions ◽  
Measure Of Noncompactness ◽  
Initial Conditions ◽  
Sufficient Conditions ◽  
Exact Controllability ◽  
Fractional Differential Inclusions ◽  
Nonlocal Initial Conditions ◽  
Fractional Differential System ◽  
Fractional Differential

The exact controllability results for Hilfer fractional differential inclusions involving nonlocal initial conditions are presented and proved. By means of the multivalued analysis, measure of noncompactness method, fractional calculus combined with the generalized Mo¨nch fixed point theorem, we derive some sufficient conditions to ensure the controllability for the nonlocal Hilfer fractional differential system. The results are new and generalize the existing results. Finally, we talk about an example to interpret the applications of our abstract results.

Fractional differential inclusions of Hilfer type under weak topologies in Banach spaces

2018 ◽  
Vol 13 (01) ◽  
pp. 2050015
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Mohamed Abdalla Darwish
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Differential Inclusions ◽  
Fractional Differential Inclusions ◽  
Measure Of Weak Noncompactness ◽  
Existence Of Weak Solutions ◽  
Mönch’S Fixed Point Theorem ◽  
Fractional Differential ◽  
Weak Topologies

In this paper, we present some results concerning the existence of weak solutions for some functional Hilfer and Hadamard fractional differential inclusions. The Mönch’s fixed point theorem and the concept of measure of weak noncompactness are the main tools used to carry out our results.

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 On the controllability of Hilfer-Katugampola fractional differential equations

2020 ◽  
Vol 24 (2) ◽  
pp. 195-204
Author(s):  
Mohamed I. Abbas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Banach Spaces ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Measure Of Noncompactness ◽  
Sufficient Conditions ◽  
Fractional Differential

By employing Kuratowski's measure of noncompactness together with Sadovskii's fixed point theorem, sufficient conditions for controllability results of Hilfer-Katugampola fractional differential equations in Banach spaces are derived.

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.

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