New Trends on the Mathematical Models and Solitons Arising in Real-World Problems, 2nd Edition

Dear Colleagues, 

The essence of mathematical tools for exemplifying the practical problems that exist in daily life is as old as the world itself. Mathematical models in science and technology have recently attracted an increased amount of research attention with the aim of understanding, describing, and predicting the future behavior of natural phenomena. Recent studies on fractional calculus have been particularly popular among researchers due to their favorable properties when analyzing real-world models associated with properties such as anomalous diffusion, non-Markovian processes, random walk, long range, and, most importantly, heterogeneous behaviors. The concept of local differential operators, along with power-law settings and non-local differential operators, was suggested in order to accurately replicate the above-cited natural processes. The complexities of nature have led mathematicians and physicists to derive the most sophisticated and scientific mathematical operators to accurately replicate and capture pragmatic realities.

Mathematical physics plays a vital role in the study of the determinants and distribution of solitons. With the help of this, we can identify wave distributions in many fields of nonlinear sciences, and many experts have recently focused their work on this field. Further, these types of studies may help us to provide the foundation for developing public policy and make regulatory decisions relating to engineering problems, as well as to evaluate both existing and new perspectives. Major areas of mathematical physics studies with mathematical models include physics, symmetry, transmission, outbreak investigation, and epidemiological problems.

This particular issue is devoted to the collection of new results, extending from theory to practice, with the aim of developing new technological tools. This Special Issue will be focused on, but not limited to:

Topics:

• Theoretical, computational, and experimental nature of mathematical physics models;
• Review performance of mathematical models with fractional differential and integral equations;
• Evaluation of models with different types of fractional operators;
• Validation of models with fractal–fractional differential and integral operators;
• Review of effect of new fractal differential and integral operators for modeling, such as epidemiological diseases, mathematical physics, soliton theory, and so on.

Prof. Dr. Haci Mehmet Baskonus
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

• mathematical physics
• partial differential equations
• epidemic models
• basic reproduction number
• fractional differential equations
• dynamical systems
• stability analysis
• bifurcation
• optimal control

• New Trends on the Mathematical Models and Solitons Arising in Real-World Problems in Symmetry (16 articles)

Title: Computational models of neurodevelopmental symmetry-breaking
Authors: Roman Bauer
Affiliation: Department of Computer Science, University of Surrey, UK
Abstract: Computational modelling of biological symmetry-breaking processes allows to formulate and compare experimentally verifiable hypotheses, as well as gain fundamental insights. In particular, neural development comprises many such symmetry-breaking phenomena which often remain poorly understood. Hence, a number of studies have produced explainable computational models that capture various symmetry-breaking processes shaping brain architecture and function. Here, I review a diverse array of computational approaches that have been used to capture intricate dynamics governing neuronal pattern formation based on cellular differentiation, neuronal arborization and the formation of synaptic connectivity. Through a comprehensive analysis of the associated models, I highlight the role of key self-organization features that drive neural asymmetry. In addition, I highlight the importance of computational modelling in addressing the challenges posed by the complexity of experimental data, and consequential value for bridging the gab between experimental observations and conceptual understanding. Overall, by surveying the interdisciplinary landscape of computational modelling in this field, a comprehensive overview is drawn of the contributions made, the pertinent challenges and the opportunities that lie ahead in unravelling the intricacies of symmetry-breaking during neural development.