scholarly journals New Existence and Uniqueness Results for Fractional Differential Equations

2013 ◽  
Vol 21 (3) ◽  
pp. 33-42 ◽  
Author(s):  
Ahmed Anber ◽  
Soumia Belarbi
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Integral Boundary Conditions ◽  
Existence Results ◽  
Banach Fixed Point Theorem ◽  
Integral Boundary ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential

AbstractIn this paper, we study a class of boundary value problems of nonlinear fractional differential equations with integral boundary conditions. Some new existence and uniqueness results are obtained by using Banach fixed point theorem. Other existence results are also presented by using Krasnoselskii theorem.

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.

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

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.

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 Results for a Class of p-Laplacian Fractional Differential Equations with Integral Boundary Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
SunAe Pak ◽  
KumSong Jong ◽  
KyuNam O ◽  
HuiChol Choi
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Integral Boundary Conditions ◽  
Contraction Mapping Principle ◽  
Laplacian Operator ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Uniqueness Results ◽  
Fractional Differential

In this paper, we investigate the existence and uniqueness of solutions for a class of integral boundary value problems of nonlinear fractional differential equations with p-Laplacian operator. We obtain some existence and uniqueness results concerned with our problem by using Schaefer’s fixed-point theorem and Banach contraction mapping principle. Finally, we present some examples to illustrate our main results.

scholarly journals Existence Results for Hilfer Fractional Differential Equations with Variable Coefficient

2021 ◽  
Vol 6 (1) ◽  
pp. 11
Author(s):  
Fang Li ◽  
Chenglong Wang ◽  
Huiwen Wang
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Variable Coefficient ◽  
Existence Results ◽  
Initial Value ◽  
Hilfer Fractional Derivative ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential

The aim of this paper is to establish the existence and uniqueness results for differential equations of Hilfer-type fractional order with variable coefficient. Firstly, we establish the equivalent Volterra integral equation to an initial value problem for a class of nonlinear fractional differential equations involving Hilfer fractional derivative. Secondly, we obtain the existence and uniqueness results for a class of Hilfer fractional differential equations with variable coefficient. We verify our results by providing two examples.

scholarly journals Integral Boundary Value Problems for Implicit Fractional Differential Equations Involving Hadamard and Caputo-Hadamard fractional Derivatives

2021 ◽  
Vol 45 (03) ◽  
pp. 331-341
Author(s):  
P. KARTHIKEYAN ◽  
R. ARUL
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Integral Boundary ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential ◽  
Integral Boundary Value Problems ◽  
Implicit Fractional Differential Equations

In this paper, we examine the existence and uniqueness of integral boundary value problem for implicit fractional differential equations (IFDE’s) involving Hadamard and Caputo-Hadamard fractional derivative. We prove the existence and uniqueness results by utilizing Banach and Schauder’s fixed point theorem. Finally, examples are introduced of our results.

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

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.

scholarly journals Study of a Class of Generalized Multiterm Fractional Differential Equations with Generalized Fractional Integral Boundary Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Wafa Shammakh ◽  
Hadeel Z. Alzumi ◽  
Zahra Albarqi
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Fixed Point Theory ◽  
Integral Boundary Conditions ◽  
Point Theory ◽  
Integral Boundary ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential

The aim of this work is to study the new generalized fractional differential equations involving generalized multiterms and equipped with multipoint boundary conditions. The nonlinear term is taken from Orlicz space. The existence and uniqueness results, with the help of contemporary tools of fixed point theory, are investigated. The Ulam stability of our problem is also presented. The obtained results are well illustrated by examples.

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