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.

Semilinear fractional order integro-differential inclusions with infinite delay

2018 ◽  
Vol 25 (3) ◽  
pp. 317-327 ◽  
Author(s):  
Khalida Aissani ◽  
Mouffak Benchohra ◽  
Mohamed Abdalla Darwish
Keyword(s):  
Banach Spaces ◽  
Fractional Order ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Sufficient Conditions ◽  
Multivalued Maps ◽  
Nonlinear Alternative

AbstractIn this paper, we study the existence of mild solutions for a class of semilinear fractional order integro-differential inclusions with infinite delay in Banach spaces. Sufficient conditions for the existence of solutions are derived by using a nonlinear alternative of Leray–Schauder type for multivalued maps due to Martelli. An example is given to illustrate the theory.

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.

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 Impulsive partial hyperbolic differential inclusions of fractional order

2010 ◽  
Vol 43 (4) ◽  
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra
Keyword(s):  
Fixed Point ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Caputo Fractional Derivative ◽  
Differential Inclusions ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Hyperbolic Differential Inclusions

AbstractIn this paper we investigate the existence of solutions of a class of partial impulsive hyperbolic differential inclusions involving the Caputo fractional derivative. Our main tools are appropriate fixed point theorems from multivalued analysis.

scholarly journals Analysis of Multiterm Initial Value Problems with Caputo–Fabrizio Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Mohammed Al-Refai ◽  
Muhammed Syam
Keyword(s):  
Laplace Transform ◽  
Fractional Derivative ◽  
Initial Value Problems ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Initial Value ◽  
The Laplace Transform ◽  
Necessary And Sufficient

In this paper, we discuss the solvability of a class of multiterm initial value problems involving the Caputo–Fabrizio fractional derivative via the Laplace transform. We derive necessary and sufficient conditions to guarantee the existence of solutions to the problem. We also obtain the solutions in closed forms. We present two examples to illustrate the validity of the obtained results.

scholarly journals Nonlinear Impulsive Multi-Order Caputo-Type Generalized Fractional Differential Equations with Infinite Delay

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1108 ◽  
Author(s):  
Bashir Ahmad ◽  
Madeaha Alghanmi ◽  
Ahmed Alsaedi ◽  
Ravi P. Agarwal
Keyword(s):  
Contraction Mapping ◽  
Existence Result ◽  
Existence Of Solutions ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Contraction Mapping Principle ◽  
Initial Value ◽  
Uniqueness Of Solutions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Fractional Differential

We establish sufficient conditions for the existence of solutions for a nonlinear impulsive multi-order Caputo-type generalized fractional differential equation with infinite delay and nonlocal generalized integro-initial value conditions. The existence result is proved by means of Krasnoselskii’s fixed point theorem, while the contraction mapping principle is employed to obtain the uniqueness of solutions for the problem at hand. The paper concludes with illustrative examples.

Existence of solutions to initial value problems for nonlinear fractional differential equations on the semi-axis

2013 ◽  
Vol 16 (3) ◽  
Author(s):  
Tiberiu Trif
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Initial Value Problems ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Growth Conditions ◽  
Initial Value ◽  
Nonlinear Fractional Differential Equations ◽  
Global Existence Of Solutions ◽  
Fractional Differential

AbstractThe purpose of the paper is to investigate the global existence of solutions to initial value problems for nonlinear fractional differential equations on the semi-axis. More precisely, it deals with the initial value problem (*)$\left\{ \begin{gathered} D_{0 + }^\alpha x(t) = f(t,x(t)),t \in [0,\infty ], \hfill \\ \lim _{t \to 0 + } t^{1 - \alpha } x(t) = x_0 , \hfill \\ \end{gathered} \right. $ where 0 < α < 1, D 0+α denotes the Riemann-Liouville fractional derivative of order α, and f: (0,∞) × ℝ → ℝ is a continuous function. Unlike all the previous papers dealing with the problem of existence of solutions to (*), this problem is solved here by constructing a special locally convex space which is metrizable and complete. Then Schauder’s fixed point theorem enables to provide sufficient conditions on f, ensuring that (*) possesses at least one solution. The growth conditions imposed to f are weaker than other similar conditions already used in the literature.

scholarly journals Existence of Mild Solutions for Impulsive Fractional Stochastic Differential Inclusions with State-Dependent Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Toufik Guendouzi ◽  
Ouahiba Benzatout
Keyword(s):  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Mild Solutions ◽  
Sufficient Conditions ◽  
Multivalued Maps ◽  
State Dependent ◽  
Nonlinear Alternative ◽  
Stochastic Differential Inclusions ◽  
State Dependent Delay

We study the existence of mild solutions for a class of impulsive fractional stochastic differential inclusions with state-dependent delay. Sufficient conditions for the existence of solutions are derived by using the nonlinear alternative of Leray-Schauder type for multivalued maps due to O’Regan. An example is given to illustrate the theory.

scholarly journals Existence of Solutions for Fractional-Order Neutral Differential Inclusions with Impulsive and Nonlocal Conditions

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Chao Song ◽  
Tao Zhu ◽  
Jinde Cao
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fractional Order ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Multivalued Maps ◽  
Impulsive Differential Inclusions ◽  
Theoretical Results

This paper investigates the existence of solutions for fractional-order neutral impulsive differential inclusions with nonlocal conditions. Utilizing the fractional calculus and fixed point theorem for multivalued maps, new sufficient conditions are derived for ensuring the existence of solutions. The obtained results improve and generalize some existed results. Finally, an illustrative example is given to show the effectiveness of theoretical results.

Sign in / Sign up

Export Citation Format

Share Document