scholarly journals Existence theory and stability analysis to a coupled nonlinear fractional mixed boundary value problem

2021 ◽  
Author(s):  
Shahid Saifullah ◽  
Akbar Zada ◽  
Sumbel Shahid
Keyword(s):  
Boundary Value Problem ◽  
Mixed Type ◽  
Fixed Point Theorems ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Coupled System ◽  
Existence Theory ◽  
Nonlinear Coupled System ◽  
Fractional Differential ◽  
Type Boundary

In this manuscript, we conclude a comprehensive approach to a class of nonlinear coupled system of fractional differential equations with mixed type boundary value problem. Subsequently, the solution of coupled system exists and unique under mixed type boundary value conditions with the reference of Schaefer and Banach fixed-point theorems. Further, we developed the Hyers- Ulam stability for the considered problem. Finally, we set an example for the support of our results.

On a fractional differential inclusion with “maxima”

2016 ◽  
Vol 19 (5) ◽  
Author(s):  
Aurelian Cernea
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Differential Inclusion ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Existence Results ◽  
Fractional Differential Inclusion ◽  
Right Hand ◽  
Fractional Differential ◽  
The Right

Abstract We study a boundary value problem associated to a fractional differential inclusion with “maxima”. Several existence results are obtained by using suitable fixed point theorems when the right hand side has convex or non convex values.

scholarly journals Existence Results for the Solution of the Hybrid Caputo–Hadamard Fractional Differential Problems Using Dhage’s Approach

2021 ◽  
Vol 6 (1) ◽  
pp. 17
Author(s):  
Muhammad Yaseen ◽  
Sadia Mumtaz ◽  
Reny George ◽  
Azhar Hussain
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Existence Results ◽  
Fractional Boundary Value Problem ◽  
Numerical Examples ◽  
Fractional Differential

In this work, we explore the existence results for the hybrid Caputo–Hadamard fractional boundary value problem (CH-FBVP). The inclusion version of the proposed BVP with a three-point hybrid Caputo–Hadamard terminal conditions is also considered and the related existence results are provided. To achieve these goals, we utilize the well-known fixed point theorems attributed to Dhage for both BVPs. Moreover, we present two numerical examples to validate our analytical findings.

scholarly journals Positive Solutions to a Fractional-Order Two-Point Boundary Value Problem with p-Laplacian Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Xiangshan Kong ◽  
Haitao Li
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Operator Equation ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Laplacian Operator ◽  
Point Boundary ◽  
Fractional Differential ◽  
Multiplicity Of Positive Solutions

This paper systematically investigates positive solutions to a kind of two-point boundary value problem (BVP) for nonlinear fractional differential equations with p-Laplacian operator and presents a number of new results. First, the considered BVP is converted to an operator equation by using the property of the Caputo derivative. Second, based on the operator equation and some fixed point theorems, several sufficient conditions are presented for the nonexistence, the uniqueness, and the multiplicity of positive solutions. Finally, several illustrative examples are given to support the obtained new results. The study of illustrative examples shows that the obtained results are effective.

Tripled fixed point theorems and applications to a fractional differential equation boundary value problem

2017 ◽  
Vol 10 (03) ◽  
pp. 1750056 ◽  
Author(s):  
Hojjat Afshari ◽  
Alireza Kheiryan
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Boundary Value Problem ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Tripled Fixed Point ◽  
Equation Boundary ◽  
Fractional Differential

In this article we study a class of mixed monotone operators with convexity on ordered Banach spaces and present some new tripled fixed point theorems by means of partial order theory, we get the existence and uniqueness of tripled fixed points without assuming the operator to be compact or continuous, which extend the existing corresponding results. As applications, we utilize the results obtained in this paper to study the existence and uniqueness of positive solutions for a fractional differential equation boundary value problem.

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