On Impulsive Hyperbolic Differential Inclusions with Nonlocal Initial Conditions

2008 ◽  
Vol 140 (3) ◽  
pp. 431-442 ◽  
Author(s):  
Y.-K. Chang ◽  
J. J. Nieto ◽  
W.-S. Li
Keyword(s):  
Differential Inclusions ◽  
Initial Conditions ◽  
Nonlocal Initial Conditions ◽  
Hyperbolic 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.

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 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 One Sided Lipschitz Evolution Inclusions in Banach Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3265
Author(s):  
Ali N. A. Koam ◽  
Tzanko Donchev ◽  
Alina I. Lazu ◽  
Muhammad Rafaqat ◽  
Ali Ahmad
Keyword(s):  
Banach Spaces ◽  
Lipschitz Condition ◽  
Differential Inclusions ◽  
Initial Conditions ◽  
Lipschitz Constant ◽  
Evolution Inclusions ◽  
Nonlocal Initial Conditions ◽  
Limit Solution ◽  
The Right ◽  
Dissipative Differential Inclusions

Using the notion of limit solution, we study multivalued perturbations of m-dissipative differential inclusions with nonlocal initial conditions. These solutions enable us to work in general Banach spaces, in particular L1. The commonly used Lipschitz condition on the right-hand side is weakened to a one-sided Lipschitz one. No compactness assumptions are required. We consider the cases of an arbitrary one-sided Lipschitz condition and the case of a negative one-sided Lipschitz constant. Illustrative examples, which can be modifications of real models, are provided.

scholarly journals Fractional order differential inclusions on an unbounded domain with infinite delay

Mathematica ◽  
2020 ◽  
Vol 62 (85) (2) ◽  
pp. 167-178
Author(s):  
Mohamed Helal
Keyword(s):  
Fractional Order ◽  
Initial Value Problems ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Fréchet Spaces ◽  
Initial Value ◽  
Nonlinear Alternative ◽  
Hyperbolic Differential Inclusions

We provide sufficient conditions for the existence of solutions to initial value problems, for partial hyperbolic differential inclusions of fractional order involving Caputo fractional derivative with infinite delay by applying the nonlinear alternative of Frigon type for multivalued admissible contraction in Frechet spaces.

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