EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR A SINGULAR SYSTEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH INTEGRAL BOUNDARY CONDITIONS

2013 ◽  
Vol 31 (5_6) ◽  
pp. 877-894
Author(s):  
Lin Wang ◽  
Xinyi Lu
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Singular System ◽  
Integral Boundary Conditions ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Nonlinear Fractional Differential Equations ◽  
Fractional Differential

scholarly journals Existence and Uniqueness Results for Hadamard-Type Fractional Differential Equations with Nonlocal Fractional Integral Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Phollakrit Thiramanus ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fractional Integral ◽  
Integral Boundary Conditions ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Uniqueness Results ◽  
Fractional Differential

We study the existence and uniqueness of solutions for a fractional boundary value problem involving Hadamard-type fractional differential equations and nonlocal fractional integral boundary conditions. Our results are based on some classical fixed point theorems. Some illustrative examples are also included.

scholarly journals Existence and Uniqueness of Solutions for the System of Nonlinear Fractional Differential Equations with Nonlocal and Integral Boundary Conditions

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Yagub A. Sharifov
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Integral Boundary Conditions ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Nonlinear Fractional Differential Equations ◽  
Fractional Differential ◽  
Integral Boundary Value Problems

In the present study, the nonlocal and integral boundary value problems for the system of nonlinear fractional differential equations involving the Caputo fractional derivative are investigated. Theorems on existence and uniqueness of a solution are established under some sufficient conditions on nonlinear terms. A simple example of application of the main result of this paper is presented.

scholarly journals On Coupledp-Laplacian Fractional Differential Equations with Nonlinear Boundary Conditions

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Aziz Khan ◽  
Yongjin Li ◽  
Kamal Shah ◽  
Tahir Saeed Khan
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Integral Boundary Conditions ◽  
Coupled System ◽  
Laplacian Operator ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Fractional Differential

This paper is related to the existence and uniqueness of solutions to a coupled system of fractional differential equations (FDEs) with nonlinearp-Laplacian operator by using fractional integral boundary conditions with nonlinear term and also to checking the Hyers-Ulam stability for the proposed problem. The functions involved in the proposed coupled system are continuous and satisfy certain growth conditions. By using topological degree theory some conditions are established which ensure the existence and uniqueness of solution to the proposed problem. Further, certain conditions are developed corresponding to Hyers-Ulam type stability for the positive solution of the considered coupled system of FDEs. Also, from applications point of view, we give an example.

scholarly journals Existence and Uniqueness of Solutions for the Nonlinear Fractional Differential Equations with Two-point and Integral Boundary Conditions

2021 ◽  
Vol 14 (2) ◽  
pp. 608-617
Author(s):  
Yagub Sharifov ◽  
S.A. Zamanova ◽  
R.A. Sardarova
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Integral Boundary Conditions ◽  
Contraction Mapping Principle ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Fractional Differential

In this paper the existence and uniqueness of solutions to the fractional differential equations with two-point and integral boundary conditions is investigated. The Green function is constructed, and the problem under consideration is reduced to the equivalent integral equation. Existence and uniqueness of a solution to this problem is analyzed using the Banach the contraction mapping principle and Krasnoselskii’s fixed point theorem.

scholarly journals Existence and uniqueness of solutions for a singular system of higher-order nonlinear fractional differential equations with integral boundary conditions

2013 ◽  
Vol 18 (4) ◽  
pp. 493-518 ◽  
Author(s):  
Lin Wang ◽  
Xingqiu Zhang ◽  
Xinyi Lu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Singular System ◽  
Integral Boundary Conditions ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Fractional Differential

In this paper, we study the existence and uniqueness of solutions for a singular system of nonlinear fractional differential equations with integral boundary conditions. We obtain existence and uniqueness results of solutions by using the properties of the Green’s function, a nonlinear alternative of Leray–Schauder-type, Guo–Krasnoselskii’s fixed point theorem in a cone and the Banach fixed point theorem. Some examples are included to show the applicability of our results.

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