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.

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 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 Existence and Stability Results for Second-Order Neutral Stochastic Differential Equations With Random Impulses and Poisson Jumps

2021 ◽  
Vol 1 (1) ◽  
pp. 1-18
Author(s):  
K. Ravikumar ◽  
K. Ramkumar ◽  
Dimplekumar Chalishajar
Keyword(s):  
Differential Equations ◽  
Initial Conditions ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Banach Contraction ◽  
Existence And Stability ◽  
Random Impulses ◽  
Functional Differential ◽  
The Stability ◽  
Stability Results

The objective of this paper is to investigate the existence and stability results of secondorder neutral stochastic functional differential equations (NSFDEs) in Hilbert space. Initially, we establish the existence results of mild solutions of the aforementioned system using the Banach contraction principle. The results are formulated using stochastic analysis techniques. In the later part, we investigate the stability results through the continuous dependence of solutions on initial conditions.

scholarly journals Stability of Nonlocal Stochastic Volterra Equations

2021 ◽  
Vol 7 (2) ◽  
pp. 48-55
Author(s):  
Sheila Bishop ◽  
◽  
Agatha Nnubia ◽  
Keyword(s):  
Model Equation ◽  
Initial Conditions ◽  
Sufficient Conditions ◽  
Volterra Equations ◽  
Gronwall Lemma ◽  
Stability Of Solutions ◽  
Existence And Stability ◽  
Rassias Stability

In this paper, we study Ulam-Hyers-Rassias stability of solutions for nonlocal stochastic Volterra equations. Sufficient conditions for the existence and stability of solutions are derived using the Gronwall lemma. The advantage of our model equation is that it allows for additional measurements leading to better results compared to models with local initial conditions. Examples are solved to illustrate the applications of the results.

scholarly journals Existence and Stability Results for a Fractional Order Differential Equation with Non-Conjugate Riemann-Stieltjes Integro-Multipoint Boundary Conditions

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 249 ◽  
Author(s):  
Bashir Ahmad ◽  
Ymnah Alruwaily ◽  
Ahmed Alsaedi ◽  
Sotiris K. Ntouyas
Keyword(s):  
Boundary Conditions ◽  
Fractional Order ◽  
Order Differential Equation ◽  
Fractional Order Differential Equation ◽  
Uniqueness Of Solutions ◽  
Multipoint Boundary ◽  
Existence And Stability ◽  
Multipoint Boundary Conditions ◽  
Stability Results ◽  
Rassias Stability

We discuss the existence and uniqueness of solutions for a Caputo-type fractional order boundary value problem equipped with non-conjugate Riemann-Stieltjes integro-multipoint boundary conditions on an arbitrary domain. Modern tools of functional analysis are applied to obtain the main results. Examples are constructed for the illustration of the derived results. We also investigate different kinds of Ulam stability, such as Ulam-Hyers stability, generalized Ulam-Hyers stability, and Ulam-Hyers-Rassias stability for the problem at hand.

Shelf solutions and dispersive shocks in a discrete NLS equation: Effects of nonlocality

2016 ◽  
Vol 25 (04) ◽  
pp. 1650045 ◽  
Author(s):  
Panayotis Panayotaros
Keyword(s):  
Light Propagation ◽  
Laser Light ◽  
Initial Conditions ◽  
Nls Equation ◽  
Nonlocal Nonlinearity ◽  
Waveguide Arrays ◽  
Existence And Stability ◽  
Wave Profiles ◽  
Dnls Equation ◽  
Stability Results

We study shelf-like breathers and dispersive shock phenomena in a discrete nonlinear Schrödinger (DNLS) equation with a nonlocal nonlinearity. The system models laser light propagation in waveguide arrays made from a nematic liquid crystal substratum. Shelf-like breathers are studied in the regime of small linear intersite coupling, and we report some new theoretical existence and stability results. We also study numerically the evolution from nearby dam-break and more general jump initial conditions for stronger linear intersite coupling. In the defocusing case, we see rarefaction and shock wave profiles, superposed with oscillations. Some of the hyperbolic features of the observed profiles are described approximately by continuous NLS hydrodynamics. Nonlocality is seen to lead to some smoothing of the rapid oscillations seen in the local DNLS.

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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