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 Anti-Periodic Fractional Differential Inclusions with ψ-Caupto Fractional Derivative

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Dandan Yang ◽  
Chuanzhi Bai
Keyword(s):  
Fractional Derivative ◽  
Differential Inclusions ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Fractional Differential Inclusions ◽  
Fractional Differential ◽  
Special Case ◽  
Fractional Boundary Value Problems

In this paper, we investigate the existence of solutions for a class of fractional boundary value problems with anti-periodic boundary value conditions with ψ-Caupto fractional derivative. By means of some standard fixed point theorems, sufficient conditions for the existence of solutions for the fractional differential inclusions with ψ-Caputo derivatives are presented. Our result generalizes the known special case if ψx=x and single known results to the multi-valued ones.

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 Boundary value problems for Caputo-Hadamard fractional differential inclusions with Integral Conditions

2020 ◽  
Vol 6 (1) ◽  
pp. 62-75
Author(s):  
Ahmed Zahed ◽  
Samira Hamani ◽  
Johnny Henderson
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Fractional Differential Inclusions ◽  
Integral Conditions ◽  
Right Hand ◽  
Fractional Differential

AbstractFor r ∈ (1, 2], the authors establish sufficient conditions for the existence of solutions for a class of boundary value problem for rth order Caputo-Hadamard fractional differential inclusions satisfying nonlinear integral conditions. Both cases of convex and nonconvex valued right hand sides are considered.

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 Coupled Systems of Time-Fractional Differential Problems by Using a New Fractional Derivative

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Ahmed Alsaedi ◽  
Dumitru Baleanu ◽  
Sina Etemad ◽  
Shahram Rezapour
Keyword(s):  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Coupled System ◽  
Continuous Functions ◽  
Coupled Systems ◽  
Fractional Differential Inclusions ◽  
Fractional Differential ◽  
Time Fractional Differential Equations

The existence of solutions for a coupled system of time-fractional differential equations including continuous functions and the Caputo-Fabrizio fractional derivative is examined. After that we investigated a coupled system of time-fractional differential inclusions including compact- and convex-valuedL1-Caratheodory multifunctions and the Caputo-Fabrizio fractional derivative.

Boundary Value Problems for Fractional Differential Equations

2009 ◽  
Vol 16 (3) ◽  
pp. 401-411 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Mouffak Benchohra ◽  
Samira Hamani
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Boundary Value Problems ◽  
Fractional Differential Equations ◽  
Caputo Fractional Derivative ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Fractional Differential

Abstract The sufficient conditions are established for the existence of solutions for a class of boundary value problems for fractional differential equations involving the Caputo fractional derivative.

scholarly journals Nonexistence Results for Higher Order Fractional Differential Inequalities with Nonlinearities Involving Caputo Fractional Derivative

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1866
Author(s):  
Mohamed Jleli ◽  
Bessem Samet ◽  
Calogero Vetro
Keyword(s):  
Fractional Derivative ◽  
Caputo Fractional Derivative ◽  
A Priori Estimates ◽  
Sufficient Conditions ◽  
Global Solutions ◽  
Higher Order ◽  
Differential Inequalities ◽  
Structure Of Solutions ◽  
Nonlinear Capacity ◽  
Fractional Differential

Higher order fractional differential equations are important tools to deal with precise models of materials with hereditary and memory effects. Moreover, fractional differential inequalities are useful to establish the properties of solutions of different problems in biomathematics and flow phenomena. In the present work, we are concerned with the nonexistence of global solutions to a higher order fractional differential inequality with a nonlinearity involving Caputo fractional derivative. Namely, using nonlinear capacity estimates, we obtain sufficient conditions for which we have no global solutions. The a priori estimates of the structure of solutions are obtained by a precise analysis of the integral form of the inequality with appropriate choice of test function.

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.

scholarly journals Solvability of control problem for fractional nonlinear differential inclusions with nonlocal conditions

2019 ◽  
Vol 24 (4) ◽  
Author(s):  
Alka Chadha ◽  
Rathinasamy Sakthivel ◽  
Swaroop Nandan Bora
Keyword(s):  
Differential Inclusions ◽  
Approximate Controllability ◽  
Measure Of Noncompactness ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Fractional Differential Inclusions ◽  
Multivalued Maps ◽  
Nonlinear Differential Inclusions ◽  
Approximately Controllable ◽  
Fractional Differential

In this paper, we study the approximate controllability of nonlocal fractional differential inclusions involving the Caputo fractional derivative of order q ∈ (1,2) in a Hilbert space. Utilizing measure of noncompactness and multivalued fixed point strategy, a new set of sufficient conditions is obtained to ensure the approximate controllability of nonlocal fractional differential inclusions when the multivalued maps are convex. Precisely, the results are developed under the assumption that the corresponding linear system is approximately controllable.  

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.

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