Positive solutions for a multi-order fractional nonlinear system with variable delays

Filomat ◽  
2018 ◽  
Vol 32 (18) ◽  
pp. 6155-6166
Author(s):  
Asma Bouaziz ◽  
Mohamed Kerker
Keyword(s):  
Fixed Point ◽  
Nonlinear System ◽  
Fractional Derivative ◽  
Positive Solution ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Variable Delays

This paper is concerned with the existence and uniqueness of the positive solution for a multiorder fractional nonlinear system with variable delays. The fractional derivative will be in the Caputo sense. The obtained results are based on some fixed point theorems.

scholarly journals Existence and uniqueness of positive solutions for nonlinear Caputo-Hadamard fractional differential equations

2021 ◽  
Vol 40 (1) ◽  
pp. 139-152
Author(s):  
Abdelouaheb Ardjouni
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Positive Solution ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Upper And Lower Solutions ◽  
Hadamard Fractional Differential Equations ◽  
Fractional Differential

We prove the existence and uniqueness of a positive solution of nonlinear Caputo-Hadamard fractional differential equations. In the process we employ the Schauder and Banach fixed point theorems and the method of upper and lower solutions to show the existence and uniqueness of a positive solution. Finally, an example is given to illustrate our results.

scholarly journals Uniqueness of Positive Solutions for a Perturbed Fractional Differential Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Chen Yang ◽  
Jieming Zhang
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Fractional Derivative ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Point Boundary ◽  
Liouville Fractional Derivative ◽  
Fractional Differential

We are concerned with the existence and uniqueness of positive solutions for the following nonlinear perturbed fractional two-point boundary value problem:D0+αu(t)+f(t,u,u',…,u(n-2))+g(t)=0, 0<t<1, n-1<α≤n, n≥2,u(0)=u'(0)=⋯=u(n-2)(0)=u(n-2)(1)=0, whereD0+αis the standard Riemann-Liouville fractional derivative. Our analysis relies on a fixed-point theorem of generalized concave operators. An example is given to illustrate the main result.

scholarly journals Positive Solution for the Nonlinear Hadamard Type Fractional Differential Equation withp-Laplacian

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Ya-ling Li ◽  
Shi-you Lin
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Continuous Function ◽  
Fractional Derivative ◽  
Positive Solution ◽  
Fractional Differential Equation ◽  
Fixed Point Theorems ◽  
Laplacian Operator ◽  
Nonlinear Fractional Differential Equation ◽  
Fractional Differential

We study the following nonlinear fractional differential equation involving thep-Laplacian operatorDβφpDαut=ft,ut,1<t<e,u1=u′1=u′e=0,Dαu1=Dαue=0, where the continuous functionf:1,e×0,+∞→[0,+∞),2<α≤3,1<β≤2.Dαdenotes the standard Hadamard fractional derivative of the orderα, the constantp>1, and thep-Laplacian operatorφps=sp-2s. We show some results about the existence and the uniqueness of the positive solution by using fixed point theorems and the properties of Green's function and thep-Laplacian operator.

scholarly journals EXISTENCE, UNIQUENESS AND STABILITY SOLUTIONS FOR NEW NONLINEAR SYSTEM OF INTEGRO-DIFFERENTIAL EQUATIONS OF VOLTERRA TYPE

2020 ◽  
Vol 9 (2) ◽  
pp. 109
Author(s):  
FARAJ YACOOB ISHAK
Keyword(s):  
Fixed Point ◽  
Nonlinear System ◽  
Differential Equations ◽  
Approximation Method ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Main Tool ◽  
Volterra Type ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

In this article, we established the existence, uniqueness and stability solutions for a nonlinear system of integro-differential equations of Volterra type in Banach spaces. Krasnoselskii Fixed point theorems and Picard approximation method are the main tool used here to establish the existence and uniqueness results. A simple example of application of the main result of this paper is presented.  

scholarly journals Analysis of boundary value problem with multi-point conditions involving Caputo-Hadamard fractional derivative

2020 ◽  
Vol 39 (6) ◽  
pp. 1555-1575
Author(s):  
Muthaiah Subramanian ◽  
Thangaraj Nandha Gopal
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Derivative ◽  
Boundary Value Problems ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Fractional Differential

We study the boundary value problems (BVPs) of the Caputo-Hadamard type fractional differential equations (FDEs) supplemented by multi-point conditions. Many new results of existence and uniqueness are obtained with the use of fixed point theorems for single-valued maps. With the help of examples, the results are well illustrated.

scholarly journals Analysis of Impulsive Boundary Value Pantograph Problems via Caputo Proportional Fractional Derivative under Mittag–Leffler Functions

2021 ◽  
Vol 5 (4) ◽  
pp. 251
Author(s):  
Bounmy Khaminsou ◽  
Weerawat Sudsutad ◽  
Chatthai Thaiprayoon ◽  
Jehad Alzabut ◽  
Songkran Pleumpreedaporn
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fractional Derivative ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Nonlinear Functional ◽  
Numerical Examples ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

This manuscript investigates an extended boundary value problem for a fractional pantograph differential equation with instantaneous impulses under the Caputo proportional fractional derivative with respect to another function. The solution of the proposed problem is obtained using Mittag–Leffler functions. The existence and uniqueness results of the proposed problem are established by combining the well-known fixed point theorems of Banach and Krasnoselskii with nonlinear functional techniques. In addition, numerical examples are presented to demonstrate our theoretical analysis.

scholarly journals Solutions for impulsive fractional pantograph differential equation via generalized anti-periodic boundary condition

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Idris Ahmed ◽  
Poom Kumam ◽  
Jamilu Abubakar ◽  
Piyachat Borisut ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Fixed Point ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Uniqueness Of The Solution ◽  
Fractional Differential

Abstract This study investigates the solutions of an impulsive fractional differential equation incorporated with a pantograph. This work extends and improves some results of the impulsive fractional differential equation. A differential equation of an impulsive fractional pantograph with a more general anti-periodic boundary condition is proposed. By employing the well-known fixed point theorems of Banach and Krasnoselskii, the existence and uniqueness of the solution of the proposed problem are established. Furthermore, two examples are presented to support our theoretical analysis.

scholarly journals Existence and Ulam stability for implicit fractional q-difference equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Nadjet Laledj ◽  
Yong Zhou
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Ulam Stability ◽  
Uniqueness Of Solutions ◽  
Stability Results ◽  
Rassias Stability

AbstractThis paper deals with some existence, uniqueness and Ulam–Hyers–Rassias stability results for a class of implicit fractional q-difference equations. Some applications are made of some fixed point theorems in Banach spaces for the existence and uniqueness of solutions, next we prove that our problem is generalized Ulam–Hyers–Rassias stable. Two illustrative examples are given in the last section.

scholarly journals Existence and Exact Asymptotic Behavior of Positive Solutions for a Fractional Boundary Value Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Habib Mâagli ◽  
Noureddine Mhadhebi ◽  
Noureddine Zeddini
Keyword(s):  
Asymptotic Behavior ◽  
Continuous Function ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Exact Asymptotic Behavior ◽  
Nonnegative Continuous Function

We establish the existence and uniqueness of a positive solution for the fractional boundary value problem , with the condition , where , and is a nonnegative continuous function on that may be singular at or .

scholarly journals POSITIVE SOLUTIONS OF A SECOND-ORDER NEUMANN BOUNDARY VALUE PROBLEM WITH A PARAMETER

2012 ◽  
Vol 86 (2) ◽  
pp. 244-253 ◽  
Author(s):  
YANG-WEN ZHANG ◽  
HONG-XU LI
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Existence And Uniqueness Theorem ◽  
Neumann Boundary Value Problem ◽  
Image Position ◽  
Continuous Dependence Of Solutions

AbstractIn this paper, we consider the Neumann boundary value problem with a parameter λ∈(0,∞): By using fixed point theorems in a cone, we obtain some existence, multiplicity and nonexistence results for positive solutions in terms of different values of λ. We also prove an existence and uniqueness theorem and show the continuous dependence of solutions on the parameter λ.

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