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.

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 On Caputo–Hadamard type coupled systems of nonconvex fractional differential inclusions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Samiha Belmor ◽  
Fahd Jarad ◽  
Thabet Abdeljawad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Coupled Systems ◽  
Fractional Differential Inclusions ◽  
Research Article ◽  
Fractional Differential

AbstractThis research article is mainly concerned with the existence of solutions for a coupled Caputo–Hadamard of nonconvex fractional differential inclusions equipped with boundary conditions. We derive our main result by applying Mizoguchi–Takahashi’s fixed point theorem with the help of $\mathcal{P}$ P -function characterizations.

scholarly journals Existence of Solutions for Some Coupled Systems of Fractional Differential Inclusions

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 700
Author(s):  
Aurelian Cernea
Keyword(s):  
Boundary Conditions ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
The State ◽  
Coupled Systems ◽  
State Variables ◽  
Fractional Differential Inclusions ◽  
Fractional Differential

We study two coupled systems of nonconvex fractional differential inclusions with certain nonlocal boundary conditions and we prove the existence of solutions in the case when the set-valued maps are Lipschitz in the state variables.

scholarly journals Investigating a Coupled Hybrid System of Nonlinear Fractional Differential Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Wiyada Kumam ◽  
Mian Bahadur Zada ◽  
Kamal Shah ◽  
Rahmat Ali Khan
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence Of Solutions ◽  
Coupled Fixed Point ◽  
Sufficient Conditions ◽  
Coupled Systems ◽  
Point Boundary ◽  
Coupled Fixed Point Theorem ◽  
Fractional Differential

We study sufficient conditions for existence of solutions to the coupled systems of higher order hybrid fractional differential equations with three-point boundary conditions. For this motive, we apply the coupled fixed point theorem of Krasnoselskii type to form adequate conditions for existence of solutions to the proposed system. We finish the paper with suitable illustrative example.

scholarly journals Existence results for fractional differential inclusions with Erdélyi-Kober fractional integral conditions

2017 ◽  
Vol 25 (2) ◽  
pp. 5-24 ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris K. Ntouyas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Fractional Integral ◽  
Existence Of Solutions ◽  
Existence Results ◽  
Fractional Differential Inclusions ◽  
Integral Conditions ◽  
Fractional Differential

Abstract In this paper, we discus the existence of solutions for Riemann- Liouville fractional differential inclusions supplemented with Erdélyi- Kober fractional integral conditions. We apply endpoint theory, Krasnoselskii’s multi-valued fixed point theorem and Wegrzyk's fixed point theorem for generalized contractions. For the illustration of our results, we include examples.

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