In the various aspects of mathematical physics, the treatment of equations that describe physical phenomena or even engineering applications, mathematical methods linked to linear or multivariate approximation play a crucial role, also with the aid of operator techniques with the related formalisms.

In this Entry Collection we want to focus on both analytical and numerical aspects related to the different families of differential and integro-differential equations that intervene in the different fields of physics and engineering.

Particular attention is paid to the aspects involving the fractional derivatives of recent use in many aspects of mathematical physics.

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Topic Review
Calculating Nonlinear Hyperbolic Evolution Equations
Benchmark calculations of high-precision numerical scheme for nonlinear hyperbolic evolution equations are demonstrated. The scheme is based on the Fourier spectral method for spatial discretization and the implicit Runge-Kutta method for time discretization.
  • 155
  • 23 May 2022
Topic Review
Oscillatory Properties of Noncanonical Neutral DDEs of Second-Order
A DDE is a single-variable differential equation, usually called time, in which the derivative of the solution at a certain time is given in terms of the values of the solution at earlier times. Moreover, if the highest-order derivative of the solution appears both with and without delay, then the DDE is called of the neutral type. The neutral DDEs have many interesting applications in various branches of applied science, as these equations appear in the modeling of many technological phenomena. The problem of studying the oscillatory and nonoscillatory properties of DDEs has been a very active area of research in the past few decades.
  • 78
  • 23 Dec 2021