scholarly journals Existence of an initial value problem for time-fractional Oldroyd-B fluid equation using Banach fixed point theorem

2021 ◽  
Author(s):  
Vo Viet TRI
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Initial Value Problem ◽  
Banach Fixed Point Theorem ◽  
Initial Value ◽  
Fluid Equation

On the stability for the fuzzy initial value problem

2020 ◽  
Vol 39 (5) ◽  
pp. 7747-7755
Author(s):  
Ngo Van Hoa ◽  
Tofigh Allahviranloo ◽  
Ho Vu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Initial Value Problem ◽  
Ulam Stability ◽  
Initial Value ◽  
The Stability ◽  
Theoretical Results ◽  
Rassias Stability

In this paper, we present the Hyers–Ulam stability and Hyers–Ulam-Rassias stability (HU-stability and HUR-stability for short) for fuzzy initial value problem (FIVP) by using fixed point theorem. We improve and extend some known results on the stability for FDEs by dropping some assumptions. Some examples illustrate the theoretical results.

Initial Value Problem of Fractional Integro-Differential Equations in Banach Space

2015 ◽  
Vol 18 (1) ◽  
Author(s):  
Adel Jawahdou
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Initial Value Problem ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Initial Value

AbstractThis paper is devoted to study the existence of solutions of nonlinear fractional integro-differential equation, via the techniques of measure of noncompactness. The investigation is based on a Schauder's fixed point theorem. The main result is less restrictive than those given in the literature. An illustrative example is given.

scholarly journals Existence Results of Initial Value Problems for Hybrid Fractional Sum-Difference Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Saowaluck Chasreechai ◽  
Thanin Sitthiwirattham
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Difference Equations ◽  
Initial Value Problem ◽  
Initial Value Problems ◽  
Existence Results ◽  
Initial Value ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Hybrid Fixed Point Theorem

We consider a hybrid fractional sum-difference initial value problem and a hybrid fractional sequential sum-difference initial value problem. The existence results of these two problems are proved by using the hybrid fixed point theorem for three operators in a Banach algebra and the generalized Krasnoselskii’s fixed point theorem, respectively.

scholarly journals On Almost Automorphic Mild Solutions for Nonautonomous Stochastic Evolution Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Jing Cui ◽  
Litan Yan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Banach Fixed Point Theorem ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Almost Automorphic ◽  
Composition Theorem

We consider a class of nonautonomous stochastic evolution equations in real separable Hilbert spaces. We establish a new composition theorem for square-mean almost automorphic functions under non-Lipschitz conditions. We apply this new composition theorem as well as intermediate space techniques, Krasnoselskii fixed point theorem, and Banach fixed point theorem to investigate the existence of square-mean almost automorphic mild solutions. Some known results are generalized and improved.

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 Uniqueness and Stability Results on Non-local Stochastic Random Impulsive Integro-Differential Equations

2021 ◽  
Vol 2 (3) ◽  
pp. 9-20
Author(s):  
VARSHINI S ◽  
BANUPRIYA K ◽  
RAMKUMAR K ◽  
RAVIKUMAR K
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Banach Fixed Point Theorem ◽  
Local Conditions ◽  
Non Local ◽  
Inequality Techniques ◽  
Stability Results

The paper is concerned with stochastic random impulsive integro-differential equations with non-local conditions. The sufficient conditions guarantees uniqueness of mild solution derived using Banach fixed point theorem. Stability of the solution is derived by incorporating Banach fixed point theorem with certain inequality techniques.

scholarly journals The Existence and Uniqueness of Solutions for a Class of Nonlinear Fractional Differential Equations with Infinite Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Azizollah Babakhani ◽  
Dumitru Baleanu ◽  
Ravi P. Agarwal
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Infinite Delay ◽  
Banach Fixed Point Theorem ◽  
Uniqueness Of Solutions ◽  
Fractional Differential

We prove the existence and uniqueness of solutions for two classes of infinite delay nonlinear fractional order differential equations involving Riemann-Liouville fractional derivatives. The analysis is based on the alternative of the Leray-Schauder fixed-point theorem, the Banach fixed-point theorem, and the Arzela-Ascoli theorem inΩ={y:(−∞,b]→ℝ:y|(−∞,0]∈ℬ}such thaty|[0,b]is continuous andℬis a phase space.

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