**Special Issue "Fractional and**

*Q*-Fractional Calculus and Their Real World Applications"Submission Deadline: 30 April 2022 (closed)

In
recent times, the use of fractional-order derivatives has become popular due to
its nonlocality property, which is an intrinsic property of many complex
systems. Various applications are in the modeling of different phenomena such
as financial modeling, viscoelasticity, nanotechnology, control theory of
dynamical systems, random walk, anomalous transport, biological modeling, and
anomalous diffusion. The topic of fractional *q*-calculus is the *q*-extension of the ordinary fractional
calculus, traced back to Euler and Gauss and later to Jackson one century ago.
In recent years there are many new developments and applications of the *q*-calculus in many areas of science such as
ordinary fractional calculus, optimal control problems, solutions of the *q*-difference equations, *q*-integral equations, *q*-fractional integral inequalities, *q*-transform analysis, cosmic strings, black
holes, conformal quantum mechanics, nuclear and high energy physics, and so on.

Starting
from the *q*-analog of Cauchy
formula, several authors started fitting the concept of *q*-fractional calculus, whereas others
continued by studying certain *q*-fractional
integrals, *q*-fractional
derivatives, *q*-spaces
of distributions and some kinds of *q*-special
functions such as -gamma functions; *q*-beta functions; *q*-hypergeometric functions, *q*-exponential functions and some others.
Recently, perhaps due to explosion in research within the ordinary fractional
calculus setting, new developments in the theory of the fractional *q*-difference calculus were made,
specifically, in the *q*-analogs
of integral and differential fractional operator properties such as the *q*-Laplace transform, *q*-wavelet transforms, *q*-Mellin transform, *q*-Whittaker transform, *q*-Natural transform, *q*-Sumudu transform to mention but a few.

This special session focuses on but not limited to the following topics:

•Fractional and *q*-fractional derivatives

•Fractional integrals and application

•Differential and Partial fractional equations of fractional order and their solutions.

• *q*- special functions and *q*-difference
equations and numeric solutions.

• Real
world applications associated with *q*- and fractional *q*-difference
equations.