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.

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 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.

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 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.

Mild solution of stochastic partial differential equation with nonlocal conditions and noncompact semigroups

2019 ◽  
Vol 69 (1) ◽  
pp. 111-124 ◽  
Author(s):  
Xuping Zhang ◽  
Pengyu Chen ◽  
Ahmed Abdelmonem ◽  
Yongxiang Li
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Stochastic Partial Differential Equation ◽  
Initial Conditions ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Growth Conditions ◽  
Partial Differential ◽  
Nonlocal Initial Conditions ◽  
Noncompactness Measure

Abstract The aim of this paper is to discuss the existence of mild solutions for a class of semilinear stochastic partial differential equation with nonlocal initial conditions and noncompact semigroups in a real separable Hilbert space. Combined with the theory of stochastic analysis and operator semigroups, a generalized Darbo’s fixed point theorem and a new estimation technique of the measure of noncompactness, we obtained the existence of mild solutions under the situation that the nonlinear term and nonlocal function satisfy some appropriate local growth conditions and a noncompactness measure condition. In addition, the condition of uniformly continuity of the nonlinearity is not required and also the strong restriction on the constants in the condition of noncompactness measure is completely deleted in this paper. An example to illustrate the feasibility of the main results is also given.

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 Existence of solutions of nonlinear integrodifferential equations with nonlocal conditions

2005 ◽  
Vol 36 (4) ◽  
pp. 327-335
Author(s):  
A. Anguraj ◽  
A. R. Navaneethan ◽  
T. S. Sukanya
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Existence Of Solutions ◽  
Initial Conditions ◽  
Existence Theorems ◽  
Nonlocal Conditions ◽  
Strong Solutions ◽  
Integrodifferential Equations ◽  
Nonlocal Initial Conditions

In this paper we prove the existence of mild and strong solutions of semilinear integrodifferential equations in Banach spaces with nonlocal initial conditions. We prove the existence theorems by using Schaefer's fixed point theorem.

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 of Solutions for Anti-Periodic Fractional Differential Inclusions Involving ψ-Riesz-Caputo Fractional Derivative

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 630
Author(s):  
Dandan Yang ◽  
Chuanzhi Bai
Keyword(s):  
Fractional Derivative ◽  
Caputo Fractional Derivative ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Fractional Differential Inclusions ◽  
Nonlinear Alternative ◽  
Contractive Map ◽  
Fractional Differential ◽  
Definition Of

In this paper, we investigate the existence of solutions for a class of anti-periodic fractional differential inclusions with ψ -Riesz-Caputo fractional derivative. A new definition of ψ -Riesz-Caputo fractional derivative of order α is proposed. By means of Contractive map theorem and nonlinear alternative for Kakutani maps, sufficient conditions for the existence of solutions to the fractional differential inclusions are given. We present two examples to illustrate our main results.

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