scholarly journals A novel stability analysis for the Darboux problem of partial differential equations via fixed point theory

2021 ◽  
Vol 6 (11) ◽  
pp. 12894-12901
Author(s):  
El-sayed El-hady ◽  
◽  
Abdellatif Ben Makhlouf
Keyword(s):  
Fixed Point ◽  
Stability Analysis ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Fixed Point Theory ◽  
Main Tool ◽  
Point Theory ◽  
Darboux Problem ◽  
Partial Differential ◽  
Stability Results

<abstract><p>We present Ulam-Hyers-Rassias (UHR) stability results for the Darboux problem of partial differential equations (DPPDEs). We employ some fixed point theorem (FPT) as the main tool in the analysis. In this manner, our results are considered as some generalized version of several earlier outcomes.</p></abstract>

scholarly journals Global existence and stability results for mild solutions of random impulsive partial integro-differential equations

Filomat ◽  
2018 ◽  
Vol 32 (2) ◽  
pp. 439-455 ◽  
Author(s):  
A. Vinodkumar ◽  
P. Indhumathi
Keyword(s):  
Fixed Point ◽  
Global Existence ◽  
Differential Equations ◽  
Continuous Dependence ◽  
Fixed Point Theory ◽  
Mild Solutions ◽  
Point Theory ◽  
Banach Contraction ◽  
Existence And Stability ◽  
Stability Results

In this paper, we discuss the global existence, uniqueness, continuous dependence and exponential stability of random impulsive partial integro-differential equations is investigated. The results are obtained by using the Leray-Schauder alternative fixed point theory and Banach Contraction Principle. Finally we give an example to illustrate our abstract results.

scholarly journals Boundary Value Problem for Caputo–Fabrizio Random Fractional Differential Equations

2020 ◽  
Vol 6 (2) ◽  
pp. 218-230
Author(s):  
Fouzia Bekada ◽  
Saïd Abbas ◽  
Mouffak Benchohra
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Random Operators ◽  
Ulam Stability ◽  
Fractional Differential ◽  
Stability Results

AbstractThis article deals with some existence of random solutions and Ulam stability results for a class of Caputo-Fabrizio random fractional differential equations with boundary conditions in Banach spaces. Our results are based on the fixed point theory and random operators. Two illustrative examples are presented in the last section.

scholarly journals Investigation of a Class of Implicit Anti-Periodic Boundary Value Problems

2021 ◽  
Vol 2 (1) ◽  
pp. 47-61
Author(s):  
Laila Hashtamand
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Fixed Point Theory ◽  
Periodic Boundary Conditions ◽  
Point Theory ◽  
Fractional Order Differential Equations ◽  
Periodic Boundary Value Problems ◽  
Stability Results

This research is devoted to studying a class of implicit fractional order differential equations ($\mathrm{FODEs}$) under anti-periodic boundary conditions ($\mathrm{APBCs}$). With the help of classical fixed point theory due to $\mathrm{Schauder}$ and $\mathrm{Banach}$, we derive some adequate results about the existence of at least one solution. Moreover, this manuscript discusses the concept of stability results including Ulam-Hyers (HU) stability, generalized Hyers-Ulam (GHU) stability, Hyers-Ulam Rassias (HUR) stability, and generalized Hyers-Ulam- Rassias (GHUR)stability. Finally, we give three examples to illustrate our results.

scholarly journals International Conference on Mathematics and its Applications in Science and Engineering (ICMASE 2020)

2020 ◽  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Harmonic Analysis ◽  
Complex Analysis ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Science And Engineering ◽  
Partial Differential ◽  
International Conference ◽  
Modern Methods

This abstract booklet includes the abstracts of the papers that have been presented at International Conference on Mathematics and its Applications in Science and Engineering (ICMASE 2020) which is held in Ankara Hacı Bayram Veli University, Ankara, Turkey between 9-10 July, 2020, via Online because of Covid 19 pandemia. The aim of this conference is to exchange ideas, discuss developments in mathematics, develop collaborations and interact with professionals and researchers from all over the world in with some of the following interesting topics: Functional Analysis, Approximation Theory, Real Analysis, Complex Analysis, Harmonic and non-Harmonic Analysis, Applied Analysis, Numerical Analysis, Geometry, Topology and Algebra, Modern Methods in Summability and Approximation, Operator Theory, Fixed Point Theory and Applications, Sequence Spaces and Matrix Transformation, Modern Methods in Summability and Approximation, Spectral Theory and Diferantial Operators, Boundary Value Problems, Ordinary and Partial Differential Equations, Discontinuous Differential Equations, Convex Analysis and its Applications, Optimization and its Application, Mathematics Education, Application on Variable Exponent Lebesgue Spaces, Applications on Differential Equations and Partial Differential Equations, Fourier Analysis, Wavelet and Harmonic Analysis Methods in Function Spaces, Applications on Computer Engineering, Flow Dynamics. However, the talks are not restricted to these subjects only. I am pleased to tell that this conference is also organized as a final multiplier event of the Rules_Math Project, supported by the EU.

Merton's Partial Differential Equation and Fixed Point Theory

1998 ◽  
Vol 105 (5) ◽  
pp. 412-420
Author(s):  
Franklin Lowenthal ◽  
Arnold Langsen ◽  
Clark T. Benson
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Partial Differential

scholarly journals Existence results of ψ-Hilfer integro-differential equations with fractional order in Banach space

2020 ◽  
Vol 19 (1) ◽  
pp. 171-192
Author(s):  
Mohammed A. Almalahi ◽  
Satish K. Panchal
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Banach Fixed Point Theorem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Mönch Fixed Point Theorem

AbstractIn this article we present the existence and uniqueness results for fractional integro-differential equations with ψ-Hilfer fractional derivative. The reasoning is mainly based upon different types of classical fixed point theory such as the Mönch fixed point theorem and the Banach fixed point theorem. Furthermore, we discuss Eα -Ulam-Hyers stability of the presented problem. Also, we use the generalized Gronwall inequality with singularity to establish continuous dependence and uniqueness of the δ-approximate solution.

scholarly journals On the probabilistic stability of some functional equations

2013 ◽  
Vol 29 (1) ◽  
pp. 125-132
Author(s):  
CLAUDIA ZAHARIA ◽  
◽  
DOREL MIHET ◽  
Keyword(s):  
Fixed Point ◽  
Functional Equations ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Quadratic Functional ◽  
Normed Spaces ◽  
Stability Of Functional Equations ◽  
The Stability ◽  
Stability Results

We establish stability results concerning the additive and quadratic functional equations in complete Menger ϕ-normed spaces by using fixed point theory. As particular cases, some theorems regarding the stability of functional equations in β - normed and quasi-normed spaces are obtained.

Coupled fractional differential systems with random effects in Banach spaces

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
O. Zentar ◽  
M. Ziane ◽  
S. Khelifa
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Existence Of Solutions ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Random Differential Equations ◽  
Liouville Fractional Derivative ◽  
Fractional Differential ◽  
Vector Valued ◽  
Abstract Formulation

Abstract The purpose of this work is to investigate the existence of solutions for a system of random differential equations involving the Riemann–Liouville fractional derivative. The existence result is established by means of a random abstract formulation to Sadovskii’s fixed point theorem principle [A. Baliki, J. J. Nieto, A. Ouahab and M. L. Sinacer, Random semilinear system of differential equations with impulses, Fixed Point Theory Appl. 2017 2017, Paper No. 27] combined with a technique based on vector-valued metrics and convergent to zero matrices. An example is also provided to illustrate our result.

scholarly journals Terminal Value Problem for Differential Equations with Hilfer–Katugampola Fractional Derivative

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 672 ◽  
Author(s):  
Mouffak Benchohra ◽  
Soufyane Bouriah ◽  
Juan J. Nieto
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Uniqueness Of Solutions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Banach Contraction ◽  
Fractional Differential ◽  
Terminal Value Problem

We present in this work the existence results and uniqueness of solutions for a class of boundary value problems of terminal type for fractional differential equations with the Hilfer–Katugampola fractional derivative. The reasoning is mainly based upon different types of classical fixed point theory such as the Banach contraction principle and Krasnoselskii’s fixed point theorem. We illustrate our main findings, with a particular case example included to show the applicability of our outcomes.

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