scholarly journals Existence theory and approximate solution to prey–predator coupled system involving nonsingular kernel type derivative

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Manar A. Alqudah ◽  
Thabet Abdeljawad ◽  
Eiman ◽  
Kamal Shah ◽  
Fahd Jarad ◽  
...  
Keyword(s):  
Approximate Solution ◽  
Approximate Analytical Solution ◽  
Coupled System ◽  
Qualitative Theory ◽  
Existence Theory ◽  
Nonlinear Coupled System ◽  
Adomian Method ◽  
The Laplace Transform ◽  
Predator System ◽  
Kernel Type

Abstract This manuscript considers a nonlinear coupled system under nonsingular kernel type derivative. The considered problem is investigated from two aspects including existence theory and approximate analytical solution. For the concerned qualitative theory, some fixed point results are used. While for approximate solution, the Laplace transform coupled with Adomian method is applied. Finally, by a pertinent example of prey–predator system, we support our results. Some graphical presentations are given using Matlab.

scholarly journals Existence theory and stability analysis to a coupled nonlinear fractional mixed boundary value problem

2021 ◽  
Author(s):  
Shahid Saifullah ◽  
Akbar Zada ◽  
Sumbel Shahid
Keyword(s):  
Boundary Value Problem ◽  
Mixed Type ◽  
Fixed Point Theorems ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Coupled System ◽  
Existence Theory ◽  
Nonlinear Coupled System ◽  
Fractional Differential ◽  
Type Boundary

In this manuscript, we conclude a comprehensive approach to a class of nonlinear coupled system of fractional differential equations with mixed type boundary value problem. Subsequently, the solution of coupled system exists and unique under mixed type boundary value conditions with the reference of Schaefer and Banach fixed-point theorems. Further, we developed the Hyers- Ulam stability for the considered problem. Finally, we set an example for the support of our results.

scholarly journals Toward the Approximate Solution for Fractional Order Nonlinear Mixed Derivative and Nonlocal Boundary Value Problems

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Hammad Khalil ◽  
Mohammed Al-Smadi ◽  
Khaled Moaddy ◽  
Rahmat Ali Khan ◽  
Ishak Hashim
Keyword(s):  
Approximate Solution ◽  
Boundary Conditions ◽  
Operational Matrix ◽  
Nonlocal Boundary ◽  
Coupled System ◽  
Nonlocal Boundary Conditions ◽  
Mixed Derivative ◽  
Test Problems ◽  
Operational Matrices ◽  
Nonlinear Coupled System

The paper is devoted to the study of operational matrix method for approximating solution for nonlinear coupled system fractional differential equations. The main aim of this paper is to approximate solution for the problem under two different types of boundary conditions,m^-point nonlocal boundary conditions and mixed derivative boundary conditions. We develop some new operational matrices. These matrices are used along with some previously derived results to convert the problem under consideration into a system of easily solvable matrix equations. The convergence of the developed scheme is studied analytically and is conformed by solving some test problems.

scholarly journals On Ulam Stability and Multiplicity Results to a Nonlinear Coupled System with Integral Boundary Conditions

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 223 ◽  
Author(s):  
Kamal Shah ◽  
Poom Kumam ◽  
Inam Ullah
Keyword(s):  
Fixed Point ◽  
Boundary Conditions ◽  
Integral Boundary Conditions ◽  
Coupled System ◽  
Existence Theory ◽  
Integral Boundary ◽  
Multiplicity Results ◽  
Nonlinear Coupled System ◽  
Cone Type ◽  
Stability Results

This manuscript is devoted to establishing existence theory of solutions to a nonlinear coupled system of fractional order differential equations (FODEs) under integral boundary conditions (IBCs). For uniqueness and existence we use the Perov-type fixed point theorem. Further, to investigate multiplicity results of the concerned problem, we utilize Krasnoselskii’s fixed-point theorems of cone type and its various forms. Stability analysis is an important aspect of existence theory as well as required during numerical simulations and optimization of FODEs. Therefore by using techniques of functional analysis, we establish conditions for Hyers–Ulam (HU) stability results for the solution of the proposed problem. The whole analysis is justified by providing suitable examples to illustrate our established results.

scholarly journals Quasi-stability and continuity of attractors for nonlinear system of wave equations

2021 ◽  
Vol 8 (1) ◽  
pp. 27-45
Author(s):  
M. M. Freitas ◽  
M. J. Dos Santos ◽  
A. J. A. Ramos ◽  
M. S. Vinhote ◽  
M. L. Santos
Keyword(s):  
Wave Equations ◽  
Coupled System ◽  
Global Attractors ◽  
Time Behavior ◽  
Exponential Attractors ◽  
Small Perturbations ◽  
Recent Approach ◽  
Nonlinear Coupled System ◽  
Long Time ◽  
External Forces

Abstract In this paper, we study the long-time behavior of a nonlinear coupled system of wave equations with damping terms and subjected to small perturbations of autonomous external forces. Using the recent approach by Chueshov and Lasiecka in [21], we prove that this dynamical system is quasi-stable by establishing a quasistability estimate, as consequence, the existence of global and exponential attractors is proved. Finally, we investigate the upper and lower semicontinuity of global attractors under autonomous perturbations.

scholarly journals Analytical solution of integro-differential equations describing the process of intense boiling of a superheated liquid

2021 ◽  
Author(s):  
Irina Alexandrova ◽  
Alexander Ivanov ◽  
Dmitri Alexandrov
Keyword(s):  
Distribution Function ◽  
Analytical Solution ◽  
Approximate Analytical Solution ◽  
Initial Distribution ◽  
Size Distribution Function ◽  
Superheated Liquid ◽  
Balance Equations ◽  
The Laplace Transform ◽  
And Shifts ◽  
Initial Distribution Function

In this article, an approximate analytical solution of an integro-differential system of equations is constructed, which describes the process of intense boiling of a superheated liquid. The kinetic and balance equations for the bubble-size distribution function and liquid temperature are solved analytically using the Laplace transform and saddle-point methods with allowance for an arbitrary dependence of the bubble growth rate on temperature. The rate of bubble appearance therewith is considered in accordance with the Dering-Volmer and Frenkel-Zeldovich-Kagan nucleation theories. It is shown that the initial distribution function decreases with increasing the dimensionless size of bubbles and shifts to their greater values with time.

scholarly journals Direct solution of uncertain bratu initial value problem

2019 ◽  
Vol 9 (6) ◽  
pp. 5075
Author(s):  
N. R. Anakira ◽  
A. H. Shather ◽  
A. F. Jameel ◽  
A. K. Alomari ◽  
A. Saaban
Keyword(s):  
Approximate Solution ◽  
Set Theory ◽  
Fuzzy Set Theory ◽  
Approximate Analytical Solution ◽  
Order System ◽  
Direct Solution ◽  
Initial Value ◽  
First Order ◽  
Bratu Equation ◽  
Variation Iteration Method

<span>In this paper, an approximate analytical solution for solving the fuzzy Bratu equation based on variation iteration method (VIM) is analyzed and modified without needed of any discretization by taking the benefits of fuzzy set theory. VIM is applied directly, without being reduced to a first order system, to obtain an approximate solution of the uncertain Bratu equation. An example in this regard have been solved to show the capacity and convenience of VIM.</span>

Sign in / Sign up

Export Citation Format

Share Document