The fractional derivatives and integrals and their potential uses have earned great importance, mainly because they have become powerful instruments with more accurate, efficient, and successful results in mathematical modelling of several complex phenomena in numerous seemingly diverse and widespread fields of science, engineering, and finance.

As the fractional dynamical systems grow, mature, and develop, it is very important to focus on the most promising novel directions that were worked out based on the novel methods and schemes handed over recently in the field. This covers many subjects from new analytical and numerical techniques and fundamental research directly related to engineering implementations.

This Special Issue aims to invite investigators, scientists, engineers, and practitioners throughout the world to submit the latest achievements and future challenges that will improve future understanding of this field. Original research and review articles are welcome.

Potential topics include but are not limited to the following:

• Fractional order mathematical modelling in physics
• Fractional operators and their applications
• Numerical methods for nonlinear differential equations of arbitrary order
• Analytical methods of fractional order differential equations
• Computational methods for dynamical systems of fractional order
• Stochastic fractional order differential equations with real world applications
• Fractional calculus applications to thermal problems
• Conservation Laws: problems related to non-linear heat and mass transfer
• Fractional fuzzy differential equations and their applications