Existence and Uniqueness Results for a Novel Complex Chaotic Fractional Order System

2019 ◽  
pp. 97-115 ◽  
Author(s):  
Ilknur Koca ◽  
A. Atangana
Keyword(s):  
Fractional Order ◽  
Existence And Uniqueness ◽  
Fractional Order System ◽  
Order System ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Novel Complex

Controllability of fractional order system with nonlinear term having integral contractor

2013 ◽  
Vol 16 (4) ◽  
Author(s):  
Surendra Kumar ◽  
Nagarajan Sukavanam
Keyword(s):  
Control Systems ◽  
Fractional Order ◽  
Mild Solution ◽  
Existence And Uniqueness ◽  
Nonlinear Term ◽  
Lipschitz Continuity ◽  
Fractional Order System ◽  
Order System ◽  
Semilinear Control Systems

AbstractIn this paper, controllability results for a class of semilinear control systems of fractional order are established. The nonlinear term is assumed to have an integral contractor which is a weaker condition than the Lipschitz continuity. The existence and uniqueness of mild solution is also proved.

On existence and uniqueness results for iterative mixed integrodifferential equation of fractional order

2020 ◽  
Vol 26 (2) ◽  
pp. 263-272
Author(s):  
S. I. Unhale ◽  
Subhash D. Kendre
Keyword(s):  
Numerical Solution ◽  
Fractional Order ◽  
Integrodifferential Equation ◽  
Approximation Method ◽  
Existence And Uniqueness ◽  
Local Existence ◽  
Integrodifferential Equations ◽  
Successive Approximation Method ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

AbstractThe objective of this work is to study the local existence, uniqueness, stability and other properties of solutions of iterative mixed integrodifferential equations of fractional order. The Successive Approximation Method is applied for the numerical solution of iterative mixed integrodifferential equations of fractional order.

scholarly journals Nonlocal boundary value problems for ψ-Hilfer fractional-order Langevin equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Cholticha Nuchpong ◽  
Sotiris K. Ntouyas ◽  
Devaraj Vivek ◽  
Jessada Tariboon
Keyword(s):  
Fractional Order ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Integral Boundary Conditions ◽  
Langevin Equations ◽  
Integral Boundary ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

AbstractIn the paper, we study a boundary value problem for a class of ψ-Hilfer fractional-order Langevin equations with multi-point integral boundary conditions. Existence and uniqueness results are established by using well-known fixed point theorems. Examples illustrating the main results are also included.

scholarly journals Existence and Ulam–Hyers Stability of a Fractional-Order Coupled System in the Frame of Generalized Hilfer Derivatives

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2543
Author(s):  
Abdulkafi M. Saeed ◽  
Mohammed S. Abdo ◽  
Mdi Begum Jeelani
Keyword(s):  
Fixed Point ◽  
Fractional Order ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Coupled System ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Special Cases ◽  
Stability Of The Solution

In this research paper, we consider a class of a coupled system of fractional integrodifferential equations in the frame of Hilfer fractional derivatives with respect to another function. The existence and uniqueness results are obtained in weighted spaces by applying Schauder’s and Banach’s fixed point theorems. The results reported here are more general than those found in the literature, and some special cases are presented. Furthermore, we discuss the Ulam–Hyers stability of the solution to the proposed system. Some examples are also constructed to illustrate and validate the main results.

The continuation of solutions to systems of Caputo fractional order differential equations

2020 ◽  
Vol 23 (2) ◽  
pp. 591-599 ◽  
Author(s):  
Cong Wu ◽  
Xinzhi Liu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Order ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Existence And Uniqueness Results ◽  
Fractional Order Differential Equations ◽  
Uniqueness Results ◽  
Schäuder Fixed Point Theorem

AbstractIn this paper, we study the continuation of solutions to systems of Caputo fractional order differential equations. The continuation is constructed and proven by using the Schauder Fixed Point Theorem. As a necessary prerequisite to the continuation, the existence and uniqueness results generalized for systems are also reviewed.

scholarly journals On Some Existence and Uniqueness Results for a Class of Equations of Order0<α≤1on Arbitrary Time Scales

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Abdourazek Souahi ◽  
Assia Guezane-Lakoud ◽  
Rabah Khaldi
Keyword(s):  
Differential Equations ◽  
Time Scales ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solution ◽  
Arbitrary Time ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential

This paper investigates the existence and uniqueness of solution for a class of nonlinear fractional differential equations of fractional order0<α≤1in arbitrary time scales. The results are established using extensions of Krasnoselskii-Krein, Rogers, and Kooi conditions.

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