scholarly journals Existence and Stability of Solutions for Hadamard-Stieltjes Fractional Integral Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Saïd Abbas ◽  
Eman Alaidarous ◽  
Mouffak Benchohra ◽  
Juan J. Nieto
Keyword(s):  
Integral Equations ◽  
Fractional Integral ◽  
Existence Result ◽  
Existence Results ◽  
Stieltjes Integral ◽  
Ulam Stability ◽  
Stability Of Solutions ◽  
Existence And Stability ◽  
Stability Results ◽  
Rassias Stability

We give some existence results and Ulam stability results for a class of Hadamard-Stieltjes integral equations. We present two results: the first one is an existence result based on Schauder’s fixed point theorem and the second one is about the generalized Ulam-Hyers-Rassias stability.

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.

scholarly journals EXISTENCE AND STABILITY RESULTS FOR FRACTIONAL DIFFERENTIAL EQUATIONS WITH TWO CAPUTO FRACTIONAL DERIVATIVES

2019 ◽  
pp. 341
Author(s):  
Mohamed Houas ◽  
Mohamed Bezziou
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Contraction Mapping ◽  
Nonlocal Boundary ◽  
Stability Of Solutions ◽  
Caputo Fractional Derivatives ◽  
Existence And Stability ◽  
Fractional Differential ◽  
Stability Results

In this paper, we discuss the existence, uniqueness and stability of solutions for a nonlocal boundary value problem of nonlinear fractional differential equations with two Caputo fractional derivatives. By applying the contraction mapping and O’Regan fixed point theorem, the existence results are obtained. We also derive the Ulam-Hyers stability of solutions. Finally, some examples are given to illustrate our results.

scholarly journals The Existence and Stability of Solutions for Vector Quasiequilibrium Problems in Topological Order Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Qi-Qing Song
Keyword(s):  
Equilibrium Problem ◽  
Existence Result ◽  
Quasi Equilibrium ◽  
Topological Order ◽  
Stability Of Solutions ◽  
Maximal Elements ◽  
Quasiequilibrium Problems ◽  
Existence And Stability ◽  
Essential Set ◽  
Vector Quasiequilibrium Problems

In a topological sup-semilattice, we established a new existence result for vector quasiequilibrium problems. By the analysis of essential stabilities of maximal elements in a topological sup-semilattice, we prove that for solutions of each vector quasi-equilibrium problem, there exists a connected minimal essential set which can resist the perturbation of the vector quasi-equilibrium problem.

scholarly journals Existence and stability of solutions for a system of quadratic integral equations in Banach algebras

2020 ◽  
Vol 19 (1) ◽  
pp. 203-218
Author(s):  
Said Baghdad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Banach Algebras ◽  
Main Tool ◽  
Stability Of Solutions ◽  
Existence And Stability ◽  
Quadratic Integral ◽  
Quadratic Integral Equations

AbstractThe aim of this paper is to prove the existence and stability of solutions of a system of quadratic integral equations in the Banach algebra of continuous and bounded functions on unbounded rectangle. The main tool used in our considerations is the multiple fixed point theorem which is a consequence of Darbo’s fixed point theorem and the technique associated with measures of noncompactness. We also present an illustrative example.

scholarly journals Ulam’s type stability of Hadamard type fractional integral equations

Filomat ◽  
2014 ◽  
Vol 28 (7) ◽  
pp. 1323-1331 ◽  
Author(s):  
Jinrong Wang ◽  
Zeng Lin
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fractional Integral ◽  
Fixed Point Method ◽  
Point Method ◽  
Singular Kernel ◽  
Compact Interval ◽  
Ulam’S Type Stability ◽  
Stability Results

In this paper, we further investigates Ulam?s type stability of Hadamard type fractional integral equations on a compact interval. We explore new conditions and develop valuable techniques to overcome the difficult from the Hadamard type singular kernel and extend the previous Ulam?s type stability results in [27] from [1, b] to [a, b] with a > 0 via fixed point method. Finally, two examples are given to illustrate our results.

scholarly journals A Generalized ML-Hyers-Ulam Stability of Quadratic Fractional Integral Equation

2021 ◽  
Vol 10 (1) ◽  
pp. 414-427
Author(s):  
Mohammed K. A. Kaabar ◽  
Vida Kalvandi ◽  
Nasrin Eghbali ◽  
Mohammad Esmael Samei ◽  
Zailan Siri ◽  
...  
Keyword(s):  
Differential Equation ◽  
Integral Equation ◽  
Differential Equations ◽  
Fractional Integral ◽  
Future Research ◽  
Ulam Stability ◽  
Science And Engineering ◽  
Fractional Integral Equation ◽  
Rassias Stability

Abstract An interesting quadratic fractional integral equation is investigated in this work via a generalized Mittag-Leffler (ML) function. The generalized ML–Hyers–Ulam stability is established in this investigation. We study both of the Hyers–Ulam stability (HUS) and ML–Hyers–Ulam–Rassias stability (ML-HURS) in detail for our proposed differential equation (DEq). Our proposed technique unifies various differential equations’ classes. Therefore, this technique can be further applied in future research works with applications to science and engineering.

scholarly journals Existence and stability results for random impulsive fractional pantograph equations

Filomat ◽  
2016 ◽  
Vol 30 (14) ◽  
pp. 3839-3854 ◽  
Author(s):  
A. Anguraj ◽  
A. Vinodkumar ◽  
K. Malar
Keyword(s):  
Continuous Dependence ◽  
Linear Growth ◽  
Initial Conditions ◽  
Growth Conditions ◽  
Differential Systems ◽  
Existence And Stability ◽  
Stability Results ◽  
Rassias Stability

In this paper, we study the existence, uniqueness, stability through continuous dependence on initial conditions and Hyers-Ulam-Rassias stability results for random impulsive fractional pantograph differential systems by relaxing the linear growth conditions. Finally examples are given to illustrate the applications of the abstract results.

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