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 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 Results for Generalized Bagley-Torvik Type Fractional Differential Inclusions with Nonlocal Initial Conditions

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Lizhen Chen ◽  
Gang Li
Keyword(s):  
Differential Inclusions ◽  
Initial Conditions ◽  
Existence Theorems ◽  
Nonlocal Conditions ◽  
Existence Results ◽  
Lipschitz Continuous ◽  
Nonlocal Initial Conditions ◽  
Nonlinear Alternative ◽  
Noncompactness Measure ◽  
Fractional Differential

In this article, we prove the existence of solutions for the generalized Bagley-Torvik type fractional order differential inclusions with nonlocal conditions. It allows applying the noncompactness measure of Hausdorff, fractional calculus theory, and the nonlinear alternative for Kakutani maps fixed point theorem to obtain the existence results under the assumptions that the nonlocal item is compact continuous and Lipschitz continuous and multifunction is compact and Lipschitz, respectively. Our results extend the existence theorems for the classical Bagley-Torvik inclusion and some related models.

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 Optimal Controls for a Class of Impulsive Katugampola Fractional Differential Equations with Nonlocal Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Xingru Chen ◽  
Haibo Gu ◽  
Yu Sun
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Existence Results ◽  
Optimal Controls ◽  
Minimizing Sequences ◽  
Fractional Differential

In this paper, we investigate a class of impulsive Katugampola fractional differential equations with nonlocal conditions in a Banach space. First, by using a fixed-point theorem, we obtain the existence results for a class of impulsive Katugampola fractional differential equations. Secondly, we derive the sufficient conditions for optimal controls by building approximating minimizing sequences of functions twice.

scholarly journals New results on Caputo fractional-order neutral differential inclusions without compactness

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Manar A. Alqudah ◽  
C. Ravichandran ◽  
Thabet Abdeljawad ◽  
N. Valliammal
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fractional Order ◽  
Weak Topology ◽  
Differential Inclusions ◽  
Fixed Point Theorems ◽  
Nonlocal Conditions ◽  
Existence Results ◽  
Neutral System

AbstractThis article deals with existence results of Caputo fractional neutral inclusions without compactness in Banach space using weak topology. In fact, for weakly sequentially closed maps we apply fixed point theorems to obtain the existence of the solution. Furthermore, the results are manifested for fractional neutral system held by nonlocal conditions. To justify the application of the reported results an illustration is presented.

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 Positive Solution of Singular Fractional Differential Equation in Banach Space

2011 ◽  
Vol 2011 ◽  
pp. 1-22 ◽  
Author(s):  
Jianxin Cao ◽  
Haibo Chen
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Fractional Differential Equation ◽  
Nonlinear Term ◽  
Existence Results ◽  
Multipoint Boundary ◽  
Fractional Differential ◽  
Multipoint Boundary Value Problem

We investigated a singular multipoint boundary value problem for fractional differential equation in Banach space. The nonlinear term is positive and singular at and (or) . Employing regularization, sequential techniques, and diagonalization methods, we obtained some new existence results of positive solution.

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.

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