Local and NonLocal Boundary value Problems

Edited by:

Nejmeddine Chorfi, PhD, King Saud University, Saudi Arabia

Vicentiu Radulescu, PhD, AGH University of Krakow, Poland

Submission Status: Open|   Submission Deadline: 1 December 2024

Boundary Value Problems is calling for submissions to our Collection on Local and NonLocal Boundary Value Problems (BVPs). This collection aims to conduct a comprehensive investigation into both local and nonlocal boundary value problems, with the following key objectives: characterization of local BVPs; exploration of nonlocal BVPs; integration and comparative analysis; and applications.

Boundary value problems (BVPs) play a pivotal role in various scientific and engineering disciplines, providing mathematical models for phenomena ranging from heat conduction to fluid dynamics and beyond. Traditionally, researchers have primarily focused on local BVPs, where the solution at a point depends only on the values of the function and its derivatives at that point. However, in recent years, there has been a growing recognition of the significance of nonlocal BVPs, where the solution involves the integration of the function over an interval rather than evaluation at a single point. This shift in focus arises from the need to model phenomena with nonlocal interactions, such as long-range interactions in materials, spatially distributed processes in biology, and fractional differential equations in physics.

The study of nonlocal BVPs has gained prominence due to its ability to capture the intricate nature of phenomena that exhibit memory effects, long-range interactions, and non-local dependencies. Understanding the mathematical properties, analytical solutions, and computational methods for nonlocal BVPs is essential for advancing our comprehension of diverse physical phenomena.

In this research proposal, we aim to conduct a comprehensive investigation into both local and nonlocal boundary value problems, with the following key objectives described in what follows.

Objectives:
1. Characterization of Local BVPs:
ï‚· Review classical methods for solving local BVPs.
ï‚· Investigate mathematical properties and solution existence for diverse local BVPs.
ï‚· Develop efficient numerical algorithms for local BVPs.

2. Exploration of Nonlocal BVPs:
ï‚· Investigate the mathematical foundations of nonlocal BVPs, including fractional calculus and integral equations.
ï‚· Examine the existence and uniqueness of solutions for various classes of nonlocal BVPs.
ï‚· Propose innovative numerical methods for solving nonlocal BVPs.

Integration and Comparative Analysis:
ï‚· Develop a unified framework that integrates local and nonlocal BVPs.
ï‚· Conduct a comparative analysis to identify scenarios where nonlocal effects significantly impact solutions.
ï‚· Assess the computational efficiency and accuracy of existing and proposed methods for both local and nonlocal BVPs.

Applications:
ï‚· Apply the unified approach to real-world problems in physics, engineering, and biology, emphasizing scenarios with mixed local and nonlocal effects.
ï‚· Evaluate the practical significance of considering both local and nonlocal aspects in modeling complex phenomena.
The central purpose of this special issue hosted by Boundary Value Problems is to attract high-level papers written by distinguished scientists all over the world. The topic is modern and very suitable for applications in many fields, including mathematical physics, engineering, Newtonian and non-Newtonian mechanics, etc.

1. Global solvability and boundedness to a attractionâ€“repulsion model with logistic source

Authors: Danqing Zhang
Citation: Boundary Value Problems 2024 2024:94
2. The algorithmic resolution of spectral-element discretization for the time-dependent Stokes problem

We consider two algorithms for the resolution of the time-dependent Stokes problem with nonstandard boundary conditions by the domain-decomposition spectral-element method. The first algorithm (Elimination met...

Authors: Henda Ouertani and Mohamed Abdelwahed
Citation: Boundary Value Problems 2024 2024:89
3. Existence of positive periodic solutions for LiÃ©nard equation with a singularity of repulsive type

Authors: Yu Zhu
Citation: Boundary Value Problems 2024 2024:85
4. On the study of three-dimensional compressible Navierâ€“Stokes equations

This work is devoted to the study of three-dimensional compressible Navierâ€“Stokes equations on unstructured meshes. The approach used is based on separating the convection and diffusion parts. The convective f...

Authors: Mohamed Abdelwahed, Rabe Bade, Hedia Chaker and Maatoug Hassine
Citation: Boundary Value Problems 2024 2024:84
5. Study of a class of fractional-order evolution hybrid differential equations using a modified Mittag-Leffler-type derivative

This work is devoted to using topological degree theory to establish a mathematical analysis for a class of fractional-order evolution hybrid differential equations using a modified Mittagâ€“Leffler-type derivat...

Authors: Kamal Shah, Thabet Abdeljawad, Bahaaeldin Abdalla and Manel Hleili
Citation: Boundary Value Problems 2024 2024:79
6. Blow-up of solutions for a system of nonlocal singular viscoelastic equations with sources and distributed delay terms

In this paper, we investigate a scenario concerning a coupled nonlocal singular viscoelastic equation with sources and distributed delay terms. By establishing suitable conditions, we have proved that a finite...

Authors: Abdelbaki Choucha, Mohammad Shahrouzi, Rashid Jan and Salah Boulaaras
Citation: Boundary Value Problems 2024 2024:77
7. Enhanced shifted Jacobi operational matrices of integrals: spectral algorithm for solving some types of ordinary and fractional differential equations

We provide here a novel approach for solving IVPs in ODEs and MTFDEs numerically by means of a class of MSJPs. Using the SCM, we build OMs for RIs and RLFI for MSJPs as part of our process. These architectures...

Authors: H. M. Ahmed
Citation: Boundary Value Problems 2024 2024:75
8. Riemann problem for multiply connected domain in Besov spaces

In this paper, we obtain conditions of the solvability of the Riemann boundary value problem for sectionally analytic functions in multiply connected domains in Besov spaces embedded into the class of continuo...

Authors: Nazarbay Bliev and Nurlan Yerkinbayev
Citation: Boundary Value Problems 2024 2024:70
9. Fractional double-phase nonlocal equation in Musielak-Orlicz Sobolev space

In this paper, we analyze the existence of solutions to a double-phase fractional equation of the Kirchhoff type in Musielak-Orlicz Sobolev space with variable exponents. Our approach is mainly based on the su...

Authors: Tahar Bouali, Rafik Guefaifia and Salah Boulaaras
Citation: Boundary Value Problems 2024 2024:68
10. Nonexistence results for a time-fractional biharmonic diffusion equation

Authors: Mohamed Jleli and Bessem Samet
Citation: Boundary Value Problems 2024 2024:66
11. On qualitative analysis of a fractional hybrid Langevin differential equation with novel boundary conditions

A hybrid system interacts with the discrete and continuous dynamics of a physical dynamical system. The notion of a hybrid system gives embedded control systems a great advantage. The Langevin differential equ...

Authors: Gohar Ali, Rahman Ullah Khan, Kamran, Ahmad Aloqaily and Nabil Mlaiki
Citation: Boundary Value Problems 2024 2024:62
12. The posteriori analysis of the spectral element discretization of the wave equation

This work focuses on discretizing a second-order linear wave equation using the implicit Euler scheme for time discretization and the spectral element method for spatial discretization. We prove that optimal a...

Authors: Nejmeddine Chorfi
Citation: Boundary Value Problems 2024 2024:60
13. Existence of periodic solutions for a class of $$(\phi _{1},\phi _{2})$$-Laplacian difference system with asymptotically $$(p,q)$$-linear conditions

Authors: Hai-yun Deng, Xiao-yan Lin and Yu-bo He
Citation: Boundary Value Problems 2024 2024:58
14. On a class of a coupled nonlinear viscoelastic Kirchhoff equations variable-exponents: global existence, blow up, growth and decay of solutions

In this work, we consider a quasilinear system of viscoelastic equations with dispersion, source, and variable exponents. Under suitable assumptions on the initial data and the relaxation functions, we obtaine...

Authors: Abdelbaki Choucha, Mohamed Haiour and Salah Boulaaras
Citation: Boundary Value Problems 2024 2024:57