Special Issue on Recent Advances in Numerical Techniques for Integer and Non-Integer Order for Partial Differential Equations Arising in Applied Sciences and Engineering
The equations governing the engineering and applied sciences problems lead to the formation of Ordinary, partial or fractional differential equations and different types of linear and nonlinear equations in general. In addition, the differential equations play an important role in modeling complicated physical, chemical and biological phenomenon such as vibrations, reaction process, ecological systems etc. The concept of differential equations has motivated a huge size of research work in the last several decades. The exact/analytical solutions of these differential equations are ideal, but due to mathematical complications, the exact/analytical solutions are possible only for simple problems with simple boundary conditions. The exact solutions of nonlinear equations arise in science and engineering are not always possible or time-consuming and thus the use of numerical approaches continuously remains an important alternative for the numerical treatment of these type equations. The numerical solutions of differential equations of integer and non-integer order have been of much importance for many years. In the last few years, tremendous progress has been made to this area, due to the development of computer technology. Although significant progress has been made, still the numerical methods are in the early stage of their development.
This Special Issue deals with the recent advances in numerical techniques for partial differential equations of integer order as well as fractional-order, especially in science and engineering, and will accept high-quality papers having original research results.
The purpose of this Special Issue is to unite mathematicians with physicists, engineers and other researchers, for whom differential equations are valuable research tools.
The topics of the Special Issue include, but are not limited to:
- Fractional modelling in real-world phenomena
- New analytical and numerical methods for differential equations
- Fractal and fractional differential equations
- Fractional derivatives with and without non-singular kernels
- Memory kernels: identification, construction, and definitions of new fractional operators
- Deterministic and stochastic fractional differential equations
- Applications in bioengineering, biology, and health sciences
- Discrete fractional calculus
- Local fractional derivatives and applications
- Variable order fractional differential equations
- Fractional optimal control problems
- Fractional calculus in modelling and controller design
- Fractional variational principles
- Fractional order diffusion models
- Heat, mass, and momentum transfer (fluid dynamics) with relaxations
- Biomechanical and biomedical applications of fractional calculus
- Fractional functional differential systems
- Fractals and related topics
- Fractional impulsive systems
- Fuzzy differential equations and their applications
- Fractal signal processing and applications
- Numerical evaluation of fractional differential equations
- Fractal theory and its last development
- Fractal spacetime and two-scale thermodynamics
Manuscript Submission Information
Submitted papers must be original and should not have been previously published nor be currently under consideration for publication elsewhere. In the meantime, the manuscripts should not be submitted anywhere else for publication prior to acceptance/rejection by this special issue. The corresponding author accepts the responsibility of releasing the material on behalf of all co-authors.
The papers should be prepared in keeping with the Instructions for Authors provided on the website of Journal of Applied Mathematics and Computational Mechanics: https://amcm.pcz.pl/?id=for_authors
All submissions will be thoroughly refereed through a single-blind peer-review process according to the high standards of Journal of Applied Mathematics and Computational Mechanics. Accepted papers will be published online with DOI directly after acceptance. The printed issue will be published upon accumulation of a sufficient number of accepted papers.
Please direct any general questions about this special issue or any administrative matters to the Guest Editor, Hijaz Ahmad (firstname.lastname@example.org).
Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39,00186 Roma, Italy
Email: email@example.com and firstname.lastname@example.org
PREDRAG S. STANIMIROVIC
Faculty of Science and Mathematics, University of Niš, Višegradska 33, Niš 18000, Serbia.
Google Scholar: https://www.researchgate.net/profile/Predrag_Stanimirovic
Department of Mathematics
Art and Science Faculty
Siirt University, Turkey
The submitted manuscripts for this special issue will be peer-reviewed before publication. To be considered for publication in this Special issue please submit your manuscript by March 31, 2023.