scholarly journals Existence and stability analysis of nonlinear sequential coupled system of Caputo fractional differential equations with integral boundary conditions

2018 ◽  
Vol 17 (1) ◽  
pp. 103-125 ◽  
Author(s):  
Akbar Zada ◽  
Mohammad Yar ◽  
Tongxing Li
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Integral Boundary Conditions ◽  
Coupled System ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Caputo Fractional Differential Equations ◽  
Existence And Stability ◽  
Fractional Differential

Abstract In this paper we study existence and uniqueness of solutions for a coupled system consisting of fractional differential equations of Caputo type, subject to Riemann–Liouville fractional integral boundary conditions. The uniqueness of solutions is established by Banach contraction principle, while the existence of solutions is derived by Leray–Schauder’s alternative. We also study the Hyers–Ulam stability of mentioned system. At the end, examples are also presented which illustrate our results.

A fully Hadamard type integral boundary value problem of a coupled system of fractional differential equations

2014 ◽  
Vol 17 (2) ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris Ntouyas
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Coupled System ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Type Integral ◽  
Fractional Differential

AbstractThis paper is concerned with the existence and uniqueness of solutions for a coupled system of Hadamard type fractional differential equations and integral boundary conditions. We emphasize that much work on fractional boundary value problems involves either Riemann-Liouville or Caputo type fractional differential equations. In the present work, we have considered a new problem which deals with a system of Hadamard differential equations and Hadamard type integral boundary conditions. The existence of solutions is derived from Leray-Schauder’s alternative, whereas the uniqueness of solution is established by Banach’s contraction principle. An illustrative example is also included.

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 On a Coupled System of Fractional Differential Equations with Four Point Integral Boundary Conditions

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 279 ◽  
Author(s):  
Nazim Mahmudov ◽  
Sameer Bawaneh ◽  
Areen Al-Khateeb
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Contraction Mapping ◽  
Integral Boundary Conditions ◽  
Coupled System ◽  
Contraction Mapping Principle ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Fractional Differential

The study is on the existence of the solution for a coupled system of fractional differential equations with integral boundary conditions. The first result will address the existence and uniqueness of solutions for the proposed problem and it is based on the contraction mapping principle. Secondly, by using Leray–Schauder’s alternative we manage to prove the existence of solutions. Finally, the conclusion is confirmed and supported by examples.

scholarly journals Existence and Uniqueness Results for a Coupled System of Caputo-Hadamard Fractional Differential Equations with Nonlocal Hadamard Type Integral Boundary Conditions

2020 ◽  
Vol 4 (2) ◽  
pp. 13 ◽  
Author(s):  
Shorog Aljoudi ◽  
Bashir Ahmad ◽  
Ahmed Alsaedi
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Nonlocal Boundary ◽  
Integral Boundary Conditions ◽  
Coupled System ◽  
Integral Boundary ◽  
Uniqueness Results ◽  
Fractional Differential

In this paper, we study a coupled system of Caputo-Hadamard type sequential fractional differential equations supplemented with nonlocal boundary conditions involving Hadamard fractional integrals. The sufficient criteria ensuring the existence and uniqueness of solutions for the given problem are obtained. We make use of the Leray-Schauder alternative and contraction mapping principle to derive the desired results. Illustrative examples for the main results are also presented.

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