In the last decade, fractional differential equations have been used effectively in modeling problems encountered in science and engineering. Research on fractional differential equations is multidisciplinary and is encountered in various fields such as biomathematics, plasma physics, control systems, mathematical biology, elasticity, quantum mechanics, fluid mechanics, optics, bioengineering, complex systems, and so on.

Modeling fractional differential equation problems and finding analytical, numerical, and exact solutions of these models is an essential phenomenon. Many mathematical methods have been improved in literature. In addition, different approaches in fractional analysis are discovered by creating different definitions of fractional derivative and integrals. Scientific research on these subjects has revealed new and different methods for fractional analysis, theory, and applications.

The aim of this Special Issue is to contribute to the new definitions, theories, and applications of the fractional derivative. In addition, we wish to contribute to the development and application of new methods for analytical, numerical, and exact solutions for problems arising in different disciplines. Original research and review articles are welcome.

Potential topics include but are not limited to the following:

• New definitions and theories in fractional calculus
• Applications of fractional calculus in science and engineering
• Fractional mathematical models in applied mathematics
• Analytical methods for fractional differential equations
• Numerical methods for fractional differential equations
• New numerical schemes for fractional operators
• Dynamic and biological systems related to fractional calculus
• Fractional differential equation in mathematical physics
• Solitary wave solutions in fractal media