scholarly journals On generalized boundary value problems for a class of fractional differential inclusions

2017 ◽  
Vol 20 (6) ◽  
Author(s):  
Irene Benedetti ◽  
Valeri Obukhovskii ◽  
Valentina Taddei
Keyword(s):  
Differential Inclusions ◽  
Nonlinear Term ◽  
Reflexive Banach Space ◽  
Mild Solutions ◽  
Linear Part ◽  
Fractional Differential Inclusions ◽  
Local Conditions ◽  
Non Local ◽  
Fractional Differential ◽  
Theoretical Results

AbstractWe prove existence of mild solutions to a class of semilinear fractional differential inclusions with non local conditions in a reflexive Banach space. We are able to avoid any kind of compactness assumptions both on the nonlinear term and on the semigroup generated by the linear part. We apply the obtained theoretical results to two diffusion models described by parabolic partial integro-differential inclusions.

scholarly journals Existence of solutions for fractional differential inclusions with initial value condition and non-instantaneous impulses

Filomat ◽  
2019 ◽  
Vol 33 (17) ◽  
pp. 5499-5510 ◽  
Author(s):  
Danfeng Luo ◽  
Zhiguo Luo
Keyword(s):  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Mean Value ◽  
Mean Value Theorem ◽  
Fractional Differential Inclusions ◽  
Initial Value ◽  
Generalized Gronwall Inequality ◽  
Nonlinear Alternative ◽  
Fractional Differential ◽  
Theoretical Results

In this paper, we mainly consider the existence of solutions for a kind of ?-Hilfer fractional differential inclusions involving non-instantaneous impulses. Utilizing another nonlinear alternative of Leray-Schauder type, we present a new constructive result for the addressed system with the help of generalized Gronwall inequality and Lagrange mean-value theorem, and some achievements in the literature can be generalized and improved. As an application, a typical example is delineated to demonstrate the effectiveness of our theoretical results.

scholarly journals On Noncompact Fractional Order Differential Inclusions with Generalized Boundary Condition and Impulses in a Banach Space

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Irene Benedetti ◽  
Valeri Obukhovskii ◽  
Valentina Taddei
Keyword(s):  
Banach Space ◽  
Differential Inclusion ◽  
Differential Inclusions ◽  
Nonlinear Term ◽  
Reflexive Banach Space ◽  
Nonlocal Conditions ◽  
Existence Results ◽  
Fractional Differential ◽  
Partial Differential Inclusion ◽  
Generalized Boundary Condition

We provide existence results for a fractional differential inclusion with nonlocal conditions and impulses in a reflexive Banach space. We apply a technique based on weak topology to avoid any kind of compactness assumption on the nonlinear term. As an example we consider a problem in population dynamic described by an integro-partial-differential inclusion.

scholarly journals Approximate Controllability for Impulsive Riemann-Liouville Fractional Differential Inclusions

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
Zhenhai Liu ◽  
Maojun Bin
Keyword(s):  
Control Systems ◽  
Differential Inclusions ◽  
Approximate Controllability ◽  
Mild Solutions ◽  
Sufficient Conditions ◽  
Fractional Power ◽  
Fractional Differential Inclusions ◽  
Multivalued Maps ◽  
Impulsive Differential Inclusions ◽  
Fractional Differential

We study the control systems governed by impulsive Riemann-Liouville fractional differential inclusions and their approximate controllability in Banach space. Firstly, we introduce thePC1-α-mild solutions for the impulsive Riemann-Liouville fractional differential inclusions in Banach spaces. Secondly, by using the fractional power of operators and a fixed point theorem for multivalued maps, we establish sufficient conditions for the approximate controllability for a class of Riemann-Liouville fractional impulsive differential inclusions, which is a generalization and continuation of the recent results on this issue. At the end, we give an example to illustrate the application of the abstract results.

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 Solvability of fractional differential inclusions with nonlocal initial conditions via resolvent family of operators

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Yong-Kui Chang ◽  
Rodrigo Ponce ◽  
Xu-Sheng Yang
Keyword(s):  
Differential Inclusions ◽  
Initial Conditions ◽  
Mild Solutions ◽  
Fractional Differential Inclusions ◽  
Resolvent Family ◽  
Nonlocal Initial Conditions ◽  
Fractional Differential

AbstractIn this paper, we consider mild solutions to fractional differential inclusions with nonlocal initial conditions. The main results are proved under conditions that (i) the multivalued term takes convex values with compactness of resolvent family of operators; (ii) the multivalued term takes nonconvex values with compactness of resolvent family of operators and (iii) the multivalued term takes nonconvex values without compactness of resolvent family of operators, respectively.

scholarly journals Solvability of Fractional Differential Inclusion with a Generalized Caputo Derivative

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Tamer Nabil
Keyword(s):  
Differential Inclusion ◽  
Caputo Derivative ◽  
Differential Inclusions ◽  
Nonlocal Conditions ◽  
Mean Value ◽  
Classical Theorem ◽  
Fractional Differential Inclusions ◽  
Alternative Approach ◽  
Fractional Differential ◽  
Theoretical Results

This paper is devoted to the investigation of a kind of generalized Caputo semilinear fractional differential inclusions with deviated-advanced nonlocal conditions. Solvability of the problem is established by means of the Leray-Schauder’s alternative approach with the help of the Lagrange mean-value classical theorem. Finally, some examples are given to delineate the efficient of theoretical results.

scholarly journals Existence results for some integro-differential equations with state-dependent nonlocal conditions in Fréchet Spaces

2020 ◽  
Vol 7 (1) ◽  
pp. 272-280
Author(s):  
Mamadou Abdoul Diop ◽  
Kora Hafiz Bete ◽  
Reine Kakpo ◽  
Carlos Ogouyandjou
Keyword(s):  
Differential Equations ◽  
Resolvent Operator ◽  
Mild Solutions ◽  
Linear Part ◽  
Nonlocal Conditions ◽  
Existence Results ◽  
Fréchet Spaces ◽  
Local Conditions ◽  
State Dependent ◽  
Darbo Fixed Point Theorem

AbstractIn this work, we present existence of mild solutions for partial integro-differential equations with state-dependent nonlocal local conditions. We assume that the linear part has a resolvent operator in the sense given by Grimmer. The existence of mild solutions is proved by means of Kuratowski’s measure of non-compactness and a generalized Darbo fixed point theorem in Fréchet space. Finally, an example is given for demonstration.

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.

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