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

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

Abstract and Applied Analysis ◽

10.1155/2015/290674 ◽

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.

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

Abstract and Applied Analysis ◽

10.1155/2014/902054 ◽

2014 ◽

Vol 2014 ◽

pp. 1-9 ◽

Cited By ~ 10

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.

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Caputo type fractional differential equations with nonlocal Riemann-Liouville and Erdélyi-Kober type integral boundary conditions

Filomat ◽

10.2298/fil1714515a ◽

2017 ◽

Vol 31 (14) ◽

pp. 4515-4529 ◽

Cited By ~ 1

Author(s):

Bashir Ahmad ◽

Sotiris Ntouyas ◽

Jessada Tariboon ◽

Ahmed Alsaedi

Keyword(s):

Differential Equations ◽

Boundary Conditions ◽

Fractional Differential Equations ◽

Fixed Point Theory ◽

Nonlocal Boundary ◽

Integral Boundary Conditions ◽

Point Theory ◽

Integral Boundary ◽

Uniqueness Results ◽

Fractional Differential

In this paper, we study nonlocal boundary value problems of nonlinear Caputo fractional differential equations supplemented with different combinations of Riemann-Liouville and Erd?lyi-Kober type fractional integral boundary conditions. By applying a variety of tools of fixed point theory, the desired existence and uniqueness results are obtained. Examples illustrating the main results are also constructed.

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Boundary value problems for Caputo fractional differential equations with nonlocal and fractional integral boundary conditions

Arabian Journal of Mathematics ◽

10.1007/s40065-020-00288-9 ◽

2020 ◽

Vol 9 (3) ◽

pp. 531-544

Author(s):

Choukri Derbazi ◽

Hadda Hammouche

Keyword(s):

Fixed Point ◽

Differential Equations ◽

Boundary Conditions ◽

Fractional Differential Equations ◽

Existence And Uniqueness ◽

Fractional Integral ◽

Integral Boundary Conditions ◽

Integral Boundary ◽

Uniqueness Results ◽

Fractional Differential

Abstract In this paper, we study the existence and uniqueness of solutions for fractional differential equations with nonlocal and fractional integral boundary conditions. New existence and uniqueness results are established using the Banach contraction principle. Other existence results are obtained using O’Regan fixed point theorem and Burton and Kirk fixed point. In addition, an example is given to demonstrate the application of our main results.

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On Coupledp-Laplacian Fractional Differential Equations with Nonlinear Boundary Conditions

Complexity ◽

10.1155/2017/8197610 ◽

2017 ◽

Vol 2017 ◽

pp. 1-9 ◽

Cited By ~ 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.

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