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

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