scholarly journals The unique solution of some operator equations via fractional differential equations

2022 ◽  
Vol 40 ◽  
pp. 1-9
Author(s):  
Hojat Afshari ◽  
L. Khoshvaghti
Keyword(s):  
Banach Space ◽  
Differential Equations ◽  
Unique Solution ◽  
Positive Solutions ◽  
Operator Equation ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Ordered Banach Space ◽  
Operator Equations ◽  
Fractional Differential

In this paper we consider the existence and uniqueness of positive solutions to the following operator equation in an ordered Banach space $E$$$A(x,x)+B(x,x)=x,~x\in P,$$where $P$ is a cone in $E$. We study an application for fractional differential equations.

Existence and uniqueness of positive solutions for boundary value problems of fractional differential equations

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2675-2682 ◽  
Author(s):  
Hojjat Afshari ◽  
Hamidreza Marasi ◽  
Hassen Aydi
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Monotone Operators ◽  
Fractional Differential ◽  
Mixed Monotone Operators

By using fixed point results of mixed monotone operators on cones and the concept of ?-concavity, we study the existence and uniqueness of positive solutions for some nonlinear fractional differential equations via given boundary value problems. Some concrete examples are also provided illustrating the obtained results.

scholarly journals Existence and Uniqueness of Positive Solutions for a New System of Fractional Differential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Hongyu Li ◽  
Yang Chen
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Integral Boundary Conditions ◽  
Stieltjes Integral ◽  
Integral Boundary ◽  
Fractional Differential ◽  
New System

By virtue of a recent existing fixed point theorem of increasing φ−h,e-concave operator by Zhai and Wang, we consider the existence and uniqueness of positive solutions for a new system of Caputo-type fractional differential equations with Riemann–Stieltjes integral boundary conditions.

scholarly journals Analysis of a System for Linear Fractional Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Fang Wang ◽  
Zhen-hai Liu ◽  
Ping Wang
Keyword(s):  
Differential Equations ◽  
Unique Solution ◽  
Fractional Differential Equations ◽  
Constant Coefficient ◽  
Existence And Uniqueness ◽  
Diagonal Matrix ◽  
Fractional Differential ◽  
Homogeneous Linear ◽  
Linear Fractional Differential Equations

The main purpose of this paper is to obtain the unique solution of the constant coefficient homogeneous linear fractional differential equationsDt0qX(t)=PX(t),X(a)=Band the constant coefficient nonhomogeneous linear fractional differential equationsDt0qX(t)=PX(t)+D,X(a)=BifPis a diagonal matrix andX(t)∈C1-q[t0,T]×C1-q[t0,T]×⋯×C1-q[t0,T]and prove the existence and uniqueness of these two kinds of equations for anyP∈L(Rm)andX(t)∈C1-q[t0,T]×C1-q[t0,T]×⋯×C1-q[t0,T]. Then we give two examples to demonstrate the main results.

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