scholarly journals Rothe–Legendre pseudospectral method for a semilinear pseudoparabolic equation with nonclassical boundary condition

2022 ◽  
Vol 27 (1) ◽  
pp. 38-53
Author(s):  
Abdeldjalil Chattouh ◽  
Khaled Saoudi ◽  
Maroua Nouar
Keyword(s):  
Approximation Scheme ◽  
Integral Boundary Conditions ◽  
Pseudospectral Method ◽  
Practical Reasons ◽  
Pseudoparabolic Equation ◽  
Integral Boundary ◽  
Backward Euler ◽  
Uniqueness Of The Solution ◽  
Legendre Pseudospectral Method ◽  
Nonlocal Integral Boundary Conditions

A semilinear pseudoparabolic equation with nonlocal integral boundary conditions is studied in the present paper. Using Rothe method, which is based on backward Euler finitedifference schema, we designed a suitable semidiscretization in time to approximate the original problem by a sequence of standard elliptic problems. The questions of convergence of the approximation scheme as well as the existence and uniqueness of the solution are investigated. Moreover, the Legendre pseudospectral method is employed to discretize the time-discrete approximation scheme in the space direction. The main advantage of the proposed approach lies in the fact that the full-discretization schema leads to a symmetric linear algebraic system, which may be useful for theoretical and practical reasons. Finally, numerical experiments are included to illustrate the effectiveness and robustness of the presented algorithm.

scholarly journals Existence Theory for th Order Nonlocal Integral Boundary Value Problems and Extension to Fractional Case

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris K. Ntouyas ◽  
Hamed H. Alsulami
Keyword(s):  
Differential Equations ◽  
Fixed Point Theorems ◽  
Integral Boundary Conditions ◽  
Existence Theory ◽  
Uniqueness Of Solutions ◽  
Order Problem ◽  
Integral Boundary ◽  
Integral Boundary Value Problems ◽  
Nonlocal Integral Boundary Conditions ◽  
Higher Order Problem

This paper is devoted to the study of the existence and uniqueness of solutions for th order differential equations with nonlocal integral boundary conditions. Our results are based on a variety of fixed point theorems. Some illustrative examples are discussed. We also discuss the Caputo type fractional analogue of the higher-order problem of ordinary differential equations.

scholarly journals Boundary Value Problems for Hilfer Fractional Differential Inclusions with Nonlocal Integral Boundary Conditions

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1905
Author(s):  
Athasit Wongcharoen ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Differential Inclusions ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Fractional Differential ◽  
Nonlocal Integral Boundary Conditions

In this paper, we study boundary value problems for differential inclusions, involving Hilfer fractional derivatives and nonlocal integral boundary conditions. New existence results are obtained by using standard fixed point theorems for multivalued analysis. Examples illustrating our results are also presented.

scholarly journals The Uniqueness Theorem of the Solution for a Class of Differential Systems with Coupled Integral Boundary Conditions

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Shuman Meng ◽  
Yujun Cui
Keyword(s):  
Boundary Conditions ◽  
Operator Theory ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Differential Systems ◽  
Main Method ◽  
Coupled Integral Boundary Conditions ◽  
Uniqueness Of The Solution ◽  
System Of Inequalities ◽  
The Uniqueness Theorem

We discuss the uniqueness of the solution to a class of differential systems with coupled integral boundary conditions under a Lipschitz condition. Our main method is the linear operator theory and the solvability for a system of inequalities. Finally, an example is given to demonstrate the validity of our main results.

scholarly journals A Study of Nonlinear Fractionalq-Difference Equations with Nonlocal Integral Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Ahmed Alsaedi ◽  
Bashir Ahmad ◽  
Hana Al-Hutami
Keyword(s):  
Fixed Point ◽  
Boundary Conditions ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Integral Boundary Conditions ◽  
Existence Results ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Nonlocal Integral Boundary Conditions

This paper is concerned with the existence and uniqueness of solutions for a boundary value problem of nonlinear fractionalq-difference equations with nonlocal integral boundary conditions. The existence results are obtained by applying some well-known fixed point theorems and illustrated with examples.

scholarly journals On Coupled Systems for Hilfer Fractional Differential Equations with Nonlocal Integral Boundary Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Athasit Wongcharoen ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Boundary Conditions ◽  
Integral Boundary Conditions ◽  
Coupled System ◽  
Contraction Mapping Principle ◽  
Coupled Systems ◽  
Integral Boundary ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Nonlocal Integral Boundary Conditions

In this paper, we study a coupled system involving Hilfer fractional derivatives with nonlocal integral boundary conditions. Existence and uniqueness results are obtained by applying Leray-Schauder alternative, Krasnoselskii’s fixed point theorem, and Banach’s contraction mapping principle. Examples illustrating our results are also presented.

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