scholarly journals Uniqueness of Solutions of the Generalized Abel Integral Equations in Banach Spaces

2021 ◽  
Vol 5 (3) ◽  
pp. 105
Author(s):  
Chenkuan Li ◽  
Hari M. Srivastava
Keyword(s):  
Banach Spaces ◽  
Integral Equations ◽  
Coupled System ◽  
Contraction Principle ◽  
Uniqueness Of Solutions ◽  
Abel Integral Equations ◽  
Banach’S Contraction Principle

This paper studies the uniqueness of solutions for several generalized Abel’s integral equations and a related coupled system in Banach spaces. The results derived are new and based on Babenko’s approach, Banach’s contraction principle and the multivariate Mittag–Leffler function. We also present some examples for the illustration of our main theorems.

scholarly journals Uniqueness of the Hadamard-type integral equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Chenkuan Li
Keyword(s):  
Banach Spaces ◽  
Integral Equations ◽  
Coupled System ◽  
Contraction Principle ◽  
Uniqueness Of Solutions ◽  
Type Integral ◽  
Banach’S Contraction Principle

AbstractThe goal of this paper is to study the uniqueness of solutions of several Hadamard-type integral equations and a related coupled system in Banach spaces. The results obtained are new and based on Babenko’s approach and Banach’s contraction principle. We also present several examples for illustration of the main theorems.

scholarly journals New Lyapunov-type inequalities for fractional multi-point boundary value problems involving Hilfer-Katugampola fractional derivative

2021 ◽  
Vol 7 (1) ◽  
pp. 1074-1094
Author(s):  
Wei Zhang ◽  
◽  
Jifeng Zhang ◽  
Jinbo Ni
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Boundary Value Problems ◽  
Integral Equations ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Contraction Principle ◽  
Point Boundary ◽  
Fractional Differential ◽  
Banach’S Contraction Principle

<abstract><p>In this paper, we present new Lyapunov-type inequalities for Hilfer-Katugampola fractional differential equations. We first give some unique properties of the Hilfer-Katugampola fractional derivative, and then by using these new properties we convert the multi-point boundary value problems of Hilfer-Katugampola fractional differential equations into the equivalent integral equations with corresponding Green's functions, respectively. Finally, we make use of the Banach's contraction principle to derive the desired results, and give a series of corollaries to show that the current results extend and enrich the previous results in the literature.</p></abstract>

scholarly journals On the nonlinear Hadamard-type integro-differential equation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Chenkuan Li
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Continuous Functions ◽  
Contraction Principle ◽  
Uniqueness Of Solutions ◽  
Absolutely Continuous Functions ◽  
Absolutely Continuous ◽  
Integro Differential Equation ◽  
Banach’S Contraction Principle

AbstractThis paper studies uniqueness of solutions for a nonlinear Hadamard-type integro-differential equation in the Banach space of absolutely continuous functions based on Babenko’s approach and Banach’s contraction principle. We also include two illustrative examples to demonstrate the use of main theorems.

scholarly journals New results for a coupled system of ABR fractional differential equations with sub-strip boundary conditions

2021 ◽  
Vol 7 (3) ◽  
pp. 4386-4404
Author(s):  
Mohammed A. Almalahi ◽  
◽  
Satish K. Panchal ◽  
Tariq A. Aljaaidi ◽  
Fahd Jarad ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Sufficient Conditions ◽  
Coupled System ◽  
Uniqueness Of Solutions ◽  
Alternative Theorem ◽  
Fractional Differential ◽  
Mathematical Techniques ◽  
The Stability ◽  
Stability Results ◽  
Banach’S Contraction Principle

<abstract><p>In this article, we investigate sufficient conditions for the existence, uniqueness and Ulam-Hyers (UH) stability of solutions to a new system of nonlinear ABR fractional derivative of order $ 1 &lt; \varrho\leq 2 $ subjected to multi-point sub-strip boundary conditions. We discuss the existence and uniqueness of solutions with the assistance of Leray-Schauder alternative theorem and Banach's contraction principle. In addition, by using some mathematical techniques, we examine the stability results of Ulam-Hyers (UH). Finally, we provide one example in order to show the validity of our results.</p></abstract>

A note on the L-fuzzy Banach’s contraction principle

2009 ◽  
Vol 41 (5) ◽  
pp. 2399-2400 ◽  
Author(s):  
J. Martínez-Moreno ◽  
A. Roldán ◽  
C. Roldán
Keyword(s):  
Contraction Principle ◽  
Banach’S Contraction Principle

scholarly journals Existence and Ulam stability for implicit fractional q-difference equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Nadjet Laledj ◽  
Yong Zhou
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Ulam Stability ◽  
Uniqueness Of Solutions ◽  
Stability Results ◽  
Rassias Stability

AbstractThis paper deals with some existence, uniqueness and Ulam–Hyers–Rassias stability results for a class of implicit fractional q-difference equations. Some applications are made of some fixed point theorems in Banach spaces for the existence and uniqueness of solutions, next we prove that our problem is generalized Ulam–Hyers–Rassias stable. Two illustrative examples are given in the last section.

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