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Fractional and Q-Fractional Calculus and Their Real World Applications

Submission Deadline: 30 April 2022 (closed)

Guest Editors

Dr. Shrideh Al-Omari, Al-Balqa Applied University, Jordan.


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.


Fractional integrals, fractional integral inequalities,

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