Applications of Differential Equations in Sciences

Dear Colleagues,

This Special Issue is devoted to many applications of differential equations in different fields of science. Several phenomena in nature (physics, chemistry, and biology) and society (economics) result in problems leading to the study of linear and nonlinear differential equations.

It is known that many natural phenomena are not static, but depend both on the instantaneous values of given quantities and the type of their change. Such phenomena must be described mathematically with differential equations and the mathematical models built with their help. In this way, many of the fundamental laws of physics and chemistry are defined, and in biology and economics, differential equations model the behavior of systems of great complexity. In many cases, completely different problems from unrelated scientific fields can be reduced to the same differential equations. For example, the propagation of light and sound in air and of waves on a water surface can be described by the same partial differential equation: the wave equation. Heat transfer, the theory developed by Joseph Fourier at the beginning of the 19th century, is described by another partial differential equation of the second order: heat conduction. Subsequently, it turns out that many other processes can be described with the same or similar equations, such as Brownian motion (Fokker–Planck equation) or the behavior of financial markets in the Black–Scholes model.

The main topics of this Special Issue are:

• Applications in mathematical physics;
• Applications in mechanics;
• Applications in fractional calculus;
• Applications in financial mathematics;
• Applications in mathematical biology;
• Applications in numerical methods and computer science.

Prof. Dr. Angela Slavova
Prof. Dr. Nikolay K. Vitanov
Prof. Dr. Elena V. Nikolova
Guest Editors

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