scholarly journals Study on Implicit-Type Fractional Coupled System with Integral Boundary Conditions

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 300
Author(s):  
Longfei Lin ◽  
Yansheng Liu ◽  
Daliang Zhao
Keyword(s):  
Boundary Conditions ◽  
Topological Degree ◽  
Fractional Derivatives ◽  
Existence Result ◽  
Degree Theory ◽  
Integral Boundary Conditions ◽  
Coupled System ◽  
Topological Degree Theory ◽  
Caputo Fractional Derivatives ◽  
Integral Boundary

This paper is concerned with a class of implicit-type coupled system with integral boundary conditions involving Caputo fractional derivatives. First, the existence result of solutions for the considered system is obtained by means of topological degree theory. Next, Ulam–Hyers stability and generalized Ulam–Hyers stability are studied under some suitable assumptions. Finally, one example is worked out to illustrate the main results.

scholarly journals Existence Solution for Coupled System of Langevin Fractional Differential Equations of Caputo Type with Riemann–Stieltjes Integral Boundary Conditions

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2123
Author(s):  
Ahmed Salem ◽  
Lamya Almaghamsi
Keyword(s):  
Fixed Point ◽  
Boundary Conditions ◽  
Fractional Derivatives ◽  
Integral Boundary Conditions ◽  
Coupled System ◽  
Existence Results ◽  
Stieltjes Integral ◽  
Caputo Fractional Derivatives ◽  
Integral Boundary ◽  
Fractional Differential

By employing Shauder fixed-point theorem, this work tries to obtain the existence results for the solution of a nonlinear Langevin coupled system of fractional order whose nonlinear terms depend on Caputo fractional derivatives. We study this system subject to Stieltjes integral boundary conditions. A numerical example explaining our result is attached.

scholarly journals Multiple Positive Solutions for a Class of Boundary Value Problem of Fractional p , q -Difference Equations under p , q -Integral Boundary Conditions

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Yongyang Liu ◽  
Yansheng Liu
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Difference Equations ◽  
Topological Degree ◽  
Degree Theory ◽  
Integral Boundary Conditions ◽  
Multiple Positive Solutions ◽  
Topological Degree Theory ◽  
Integral Boundary

This paper is mainly concerned with a class of fractional p , q -difference equations under p , q -integral boundary conditions. Multiple positive solutions are established by using the topological degree theory and Krein–Rutman theorem. Finally, two examples are worked out to illustrate the main results.

scholarly journals Sequential Riemann–Liouville and Hadamard–Caputo Fractional Differential Systems with Nonlocal Coupled Fractional Integral Boundary Conditions

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 174
Author(s):  
Chanakarn Kiataramkul ◽  
Weera Yukunthorn ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Boundary Conditions ◽  
Fractional Integral ◽  
Integral Boundary Conditions ◽  
Contraction Mapping Principle ◽  
Uniqueness Of Solutions ◽  
Caputo Fractional Derivatives ◽  
Integral Boundary ◽  
Banach Contraction ◽  
Fractional Differential ◽  
Banach Contraction Mapping Principle

In this paper, we initiate the study of existence of solutions for a fractional differential system which contains mixed Riemann–Liouville and Hadamard–Caputo fractional derivatives, complemented with nonlocal coupled fractional integral boundary conditions. We derive necessary conditions for the existence and uniqueness of solutions of the considered system, by using standard fixed point theorems, such as Banach contraction mapping principle and Leray–Schauder alternative. Numerical examples illustrating the obtained results are also presented.

scholarly journals Sequential Derivatives of Nonlinearq-Difference Equations with Three-Pointq-Integral Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Nittaya Pongarm ◽  
Suphawat Asawasamrit ◽  
Jessada Tariboon
Keyword(s):  
Boundary Conditions ◽  
Difference Equations ◽  
Contraction Mapping ◽  
Sufficient Conditions ◽  
Degree Theory ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Quantum Numbers ◽  
Derivatives Of

This paper studies sufficient conditions for the existence of solutions to the problem of sequential derivatives of nonlinearq-difference equations with three-pointq-integral boundary conditions. Our results are concerned with several quantum numbers of derivatives and integrals. By using Banach's contraction mapping, Krasnoselskii's fixed-point theorem, and Leray-Schauder degree theory, some new existence results are obtained. Two examples illustrate our results.

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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