scholarly journals A new class of mixed fractional differential equations with integral boundary conditions

2021 ◽  
Vol 7 (2) ◽  
pp. 227-247
Author(s):  
Djiab Somia ◽  
Nouiri Brahim
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Integral Boundary Conditions ◽  
Contraction Mapping Principle ◽  
Integral Boundary ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
New Class ◽  
Fractional Differential ◽  
Equivalence Result

AbstractThis paper deals with a new class of mixed fractional differential equations with integral boundary conditions. We show an important equivalence result between our problem and nonlinear integral Fredholm equation of the second kind. The existence and uniqueness of a positive solution are proved using Guo-Krasnoselskii’s fixed point theorem and Banach’s contraction mapping principle. Different types of Ulam-Hyers stability are discussed. Three examples are also given to show the applicability of our results.

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.

Existence of solutions for sequential fractional differential equations with four-point nonlocal fractional integral boundary conditions

Open Physics ◽  
2013 ◽  
Vol 11 (10) ◽  
Author(s):  
Bashir Ahmad ◽  
Ahmed Alsaedi ◽  
Hana Al-Hutami
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Fractional Integral ◽  
Existence Of Solutions ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Fractional Differential ◽  
Sequential Fractional Differential Equations

AbstractThis paper investigates the existence of solutions for a nonlinear boundary value problem of sequential fractional differential equations with four-point nonlocal Riemann-Liouville type fractional integral boundary conditions. We apply Banach’s contraction principle and Krasnoselskii’s fixed point theorem to establish the existence of results. Some illustrative examples are also presented.

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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