scholarly journals Uniqueness and existence of solutions for nonlinear fractional differential equations with two fractional orders

Mathematica ◽  
2021 ◽  
Vol 63 (86) (2) ◽  
pp. 254-267
Author(s):  
Mohamed Houas ◽  
◽  
Zoubir Dahmani ◽  
Erhan Set ◽  
◽  
...  
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Existence Of Solutions ◽  
Degree Theory ◽  
Uniqueness Of Solutions ◽  
Nonlinear Alternative ◽  
Banach’S Fixed Point Theorem ◽  
Fractional Differential ◽  
Uniqueness And Existence ◽  
Fractional Orders

We study the existence and uniqueness of solutions for integro-differential equations involving two fractional orders. By using the Banach’s fixed point theorem, Leray-Schauder’s nonlinear alternative and Leray-Schauder’s degree theory, the existence and uniqueness of solutions are obtained. Some illustrative examples are also presented.

scholarly journals System of fractional differential equations with Erdélyi-Kober fractional integral conditions

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Natthaphong Thongsalee ◽  
Sorasak Laoprasittichok ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fractional Integral ◽  
Existence Of Solutions ◽  
Integral Conditions ◽  
Liouville Type ◽  
Uniqueness Of Solutions ◽  
Fractional Differential ◽  
Banach’S Contraction Principle

AbstractIn this paper we study existence and uniqueness of solutions for a system consisting from fractional differential equations of Riemann-Liouville type subject to nonlocal Erdélyi-Kober fractional integral conditions. The existence and uniqueness of solutions is established by Banach’s contraction principle, while the existence of solutions is derived by using Leray-Schauder’s alternative. Examples illustrating our results are also presented.

scholarly journals Existence and Uniqueness Results for a Coupled System of Nonlinear Fractional Differential Equations with Antiperiodic Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Huina Zhang ◽  
Wenjie Gao
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Coupled System ◽  
Uniqueness Of Solutions ◽  
Nonlinear Fractional Differential Equations ◽  
Uniqueness Results ◽  
Nonlinear Alternative ◽  
Fractional Differential

This paper studies the existence and uniqueness of solutions for a coupled system of nonlinear fractional differential equations of orderα,β∈(4,5]with antiperiodic boundary conditions. Our results are based on the nonlinear alternative of Leray-Schauder type and the contraction mapping principle. Two illustrative examples are also presented.

scholarly journals Uniqueness and Existence of Solution for a System of Fractionalq-Difference Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Wen-Xue Zhou ◽  
Hai-zhong Liu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fractional Differential Equations ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Existence Of Solution ◽  
Nonlinear Alternative ◽  
Banach’S Fixed Point Theorem ◽  
Fractional Differential ◽  
Uniqueness And Existence

We prove the existence and uniqueness of solution for a system of fractional differential equations. Our results are based on the nonlinear alternative of Leray-Schauder type and Banach’s fixed-point theorem.

scholarly journals Existence results for some fractional differential equations related to A ∈ B(L2[a, b])

Filomat ◽  
2020 ◽  
Vol 34 (4) ◽  
pp. 1067-1074
Author(s):  
Eshkaftaki Bayati
Keyword(s):  
Integral Operator ◽  
Differential Equations ◽  
Integral Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Existence Of Solutions ◽  
Existence Results ◽  
Uniqueness Of Solutions ◽  
Volterra Integral Operator ◽  
Fractional Differential

In this paper we define the (generalized) linear Volterra integral operator on L2[a, b]. Then the problem of existence and uniqueness of solutions of the second kind Volterra integral equations, corresponding to this operator, will be answered. Finally, some applications of this work to the existence of solutions of some fractional differential equations, are given.

Existence of solutions for a system of fractional differential equations with coupled nonlocal boundary conditions

2018 ◽  
Vol 21 (2) ◽  
pp. 423-441 ◽  
Author(s):  
Bashir Ahmad ◽  
Rodica Luca
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence Of Solutions ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Fractional Integrals ◽  
Nonlinear Alternative ◽  
Coupled Boundary Conditions ◽  
Fractional Differential

AbstractWe study the existence of solutions for a system of nonlinear Caputo fractional differential equations with coupled boundary conditions involving Riemann-Liouville fractional integrals, by using the Schauder fixed point theorem and the nonlinear alternative of Leray-Schauder type. Two examples are given to support our main results.

scholarly journals The Existence and Uniqueness of Solutions and Lyapunov-Type Inequality for CFR Fractional Differential Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Xia Wang ◽  
Run Xu
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Type Inequality ◽  
Uniqueness Theorems ◽  
Initial Value ◽  
Uniqueness Of Solutions ◽  
Maximum Value ◽  
Fractional Differential ◽  
Lyapunov Type Inequality

In this paper, we research CFR fractional differential equations with the derivative of order 3<α<4. We prove existence and uniqueness theorems for CFR-type initial value problem. By Green’s function and its corresponding maximum value, we obtain the Lyapunov-type inequality of corresponding equations. As for application, we study the eigenvalue problem in the sense of CFR.

scholarly journals The Existence and Uniqueness of Solutions for a Class of Nonlinear Fractional Differential Equations with Infinite Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Azizollah Babakhani ◽  
Dumitru Baleanu ◽  
Ravi P. Agarwal
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Infinite Delay ◽  
Banach Fixed Point Theorem ◽  
Uniqueness Of Solutions ◽  
Fractional Differential

We prove the existence and uniqueness of solutions for two classes of infinite delay nonlinear fractional order differential equations involving Riemann-Liouville fractional derivatives. The analysis is based on the alternative of the Leray-Schauder fixed-point theorem, the Banach fixed-point theorem, and the Arzela-Ascoli theorem inΩ={y:(−∞,b]→ℝ:y|(−∞,0]∈ℬ}such thaty|[0,b]is continuous andℬis a phase space.

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