Mathematical Preliminaries

The main objective is to propose novel analytical and numerical techniques to find the solutions of partial, stochastic, and fractional-order differential equations arising in physical problems. Most of the physical phenomena that arise in mathematical physics and engineering fields can be best described by the nonlinear partial differential equations. The problems arise in different areas of applied mathematics, physics, and engineering, including fluid dynamics, nonlinear optics, solid mechanics, plasma physics, quantum field theory, and condensed-matter physics, can be modeled by partial differential equations [1–3]. Many problems of physical interest are described by partial differential equations. The usual procedures necessarily change the actual problems in essential ways in order to make it mathematically tractable by the conventional methods. Unfortunately, these changes necessarily deviate the actual solutions; therefore, they can differ, sometimes seriously, from the actual physical behavior. Physically accurate and correct solutions can be obtained by avoiding these limitations, which would add an important advancement to our insights into the natural behavior of physical systems. Consequently, it would potentially enhance the scientific and technological breakthroughs for solving nonlinear physical problems.