The fractional Laplacian in R d, which we write as (− Δ) α/2 with α∈(0, 2), has multiple
equivalent characterizations. Moreover, in bounded domains, boundary conditions must be …

Metal additive manufacturing is gaining immense research attention. Some of these
research efforts are associated with physics, statistical, or artificial intelligence-driven …

Fractional calculus, which has two main features—singularity and nonlocality from its origin—
means integration and differentiation of any positive real order or even complex order. It has …

Partial differential equations (PDEs) are used with huge success to model phenomena
across all scientific and engineering disciplines. However, across an equally wide swath …

The notion of general classes of operators has recently been proposed as an approach to
fractional calculus that respects pure and applied viewpoints equally. Here we demonstrate …

The concept of fractional derivative has been demonstrated to be successful when applied
to model a range of physical and real life phenomena, be it in engineering and science …

Starting with an introduction to fractional derivatives and numerical approximations, this
book presents finite difference methods for fractional differential equations, including time …

Fractional calculus, albeit a synonym of fractional integrals and derivatives which have two
main characteristics—singularity and nonlocality—has attracted increasing interest due to its …

We conduct a formal study of a particular class of fractional operators, namely weighted
fractional calculus, and its extension to the more general class known as weighted fractional …

The nonlinear Schrödinger equation is used to model various phenomena, such as solitons
self-focusing effects and rogue waves. In the ocean engineering, the modified nonlinear …