scholarly journals Existence of the Solution for System of Coupled Hybrid Differential Equations with Fractional Order and Nonlocal Conditions

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
Khalid Hilal ◽  
Ahmed Kajouni
Keyword(s):  
Differential Equations ◽  
Existence Theorem ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Differential Operators ◽  
Nonlocal Conditions ◽  
Uniqueness Result ◽  
Carathéodory Conditions ◽  
Fractional Differential ◽  
Hybrid Differential Equations

This paper is motivated by some papers treating the fractional hybrid differential equations with nonlocal conditions and the system of coupled hybrid fractional differential equations; an existence theorem for fractional hybrid differential equations involving Caputo differential operators of order1<α≤2is proved under mixed Lipschitz and Carathéodory conditions. The existence and uniqueness result is elaborated for the system of coupled hybrid fractional differential equations.

scholarly journals Existence and uniqueness results for nonlinear implicit Riemann-Liouville fractional differential equations with nonlocal conditions

Filomat ◽  
2020 ◽  
Vol 34 (14) ◽  
pp. 4881-4891
Author(s):  
Adel Lachouri ◽  
Abdelouaheb Ardjouni ◽  
Ahcene Djoudi
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Nonlocal Conditions ◽  
Point Theory ◽  
Uniqueness Of Solutions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential

In this paper, we use the fixed point theory to obtain the existence and uniqueness of solutions for nonlinear implicit Riemann-Liouville fractional differential equations with nonlocal conditions. An example is given to illustrate this work.

scholarly journals Existence and Uniqueness Results for Fractional Differential Equations with Riemann-Liouville Fractional Integral Boundary Conditions

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Mohamed I. Abbas
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fractional Integral ◽  
Integral Boundary Conditions ◽  
Uniqueness Result ◽  
Integral Boundary ◽  
Uniqueness Results ◽  
Fractional Differential

We prove the existence and uniqueness of solution for fractional differential equations with Riemann-Liouville fractional integral boundary conditions. The first existence and uniqueness result is based on Banach’s contraction principle. Moreover, other existence results are also obtained by using the Krasnoselskii fixed point theorem. An example is given to illustrate the main results.

scholarly journals Existence Results for a System of Coupled Hybrid Differential Equations with Fractional Order

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Mohamed Hannabou ◽  
Khalid Hilal
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Existence Of Solutions ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Uniqueness Result ◽  
Existence Results ◽  
Fractional Differential ◽  
Hybrid Differential Equations

This paper studies the existence of solutions for a system of coupled hybrid fractional differential equations. We make use of the standard tools of the fixed point theory to establish the main results. The existence and uniqueness result is elaborated with the aid of an example.

scholarly journals The Use of Fractional B-Splines Wavelets in Multiterms Fractional Ordinary Differential Equations

2010 ◽  
Vol 2010 ◽  
pp. 1-13 ◽  
Author(s):  
X. Huang ◽  
X. Lu
Keyword(s):  
Differential Equations ◽  
Asymptotic Solution ◽  
Explicit Expression ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Differential Operators ◽  
Positive Real ◽  
B Splines ◽  
Fractional Differential ◽  
Linear Differential

We discuss the existence and uniqueness of the solutions of the nonhomogeneous linear differential equations of arbitrary positive real order by using the fractional B-Splines wavelets and the Mittag-Leffler function. The differential operators are taken in the Riemann-Liouville sense and the initial values are zeros. The scheme of solving the fractional differential equations and the explicit expression of the solution is given in this paper. At last, we show the asymptotic solution of the differential equations of fractional order and corresponding truncated error in theory.

scholarly journals Existence and Stability Analysis for Fractional Differential Equations with Mixed Nonlocal Conditions

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 117 ◽  
Author(s):  
Suphawat Asawasamrit ◽  
Woraphak Nithiarayaphaks ◽  
Sotiris Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Nonlocal Conditions ◽  
Ulam Stability ◽  
Existence And Stability ◽  
Fractional Differential ◽  
Mixed Fractional Derivatives

In this paper, we study the existence and uniqueness of solution for fractional differential equations with mixed fractional derivatives, integrals and multi-point conditions. After that, we also establish different kinds of Ulam stability for the problem at hand. Examples illustrating our results are also presented.

scholarly journals Nonlinear Random Differential Equations with n Sequential Fractional Derivatives

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Yfrah Hafssa ◽  
Zoubir Dahmani
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Nonlocal Conditions ◽  
Uniqueness Of Solutions ◽  
Random Data ◽  
Banach Contraction ◽  
Random Differential Equations ◽  
Fractional Differential

Abstract This article deals with a solvability for a problem of random fractional differential equations with n sequential derivatives and nonlocal conditions. The existence and uniqueness of solutions for the problem is obtained by using Banach contraction principle. New random data concepts for the considered problem are introduced and some related definitions are given. Also, some results related to the dependance on the introduced data are established for both random and deterministic cases.

Sign in / Sign up

Export Citation Format

Share Document