Fractional differential equations (or briefly a FPDE) are a very robust mathematical instrument to describe many phenomena with local and nonlocal behavior in different areas of research. FPDEs are indispensable in modeling various phenomena and processes in natural, engineering, and social sciences. Furthermore, they describe physical events such as sound, heat, electrodynamics, fluid dynamics, electrostatics, elasticity, electrostatics, electrodynamics, gravity, diffusion, quantum mechanics, etc. Exact solutions represent rigorous standards that help to better understand the properties and qualitative features of fractional differential equations. They allow one to test thoroughly and accurately, numerous computational, numerical, and approximate analytical procedures for solving these equations. Therefore, different computational techniques are extensively employed to assist in predicting the future behaviors of these equations. Thanks to their vast implementation and their functionality for solving nonlinear problems, scientists studying in this area have developed many methods. Lately, many differential and integral operators have been accepted as exceptional mathematical tools to reproduce recognized facts.

The aim of this special issue is to gather numerous articles on various mathematical tools in studies on fractional differential equations, optimization and their applications. However, all these apparently different applications have a common mathematical description under the form of nonlinear fractional equations or nonlinear systems of fractional differential equations, possibly containing higher order derivative terms, nonlinear operators, and nonlinear source terms. Equally welcome are relevant topics related to symmetry reduction, the development and refinement of methods for finding exact solutions, and new applications of exact solutions. The Special Issue can also serve as a platform for exchanging ideas between scientists interested in fractional differential equations. We welcome original research and review articles.

Potential topics include but are not limited to the following:

• New computational methods for fractional differential equations
• Symmetry reductions
• Advanced exact solutions of fractional differential equations
• Implementation of mathematical models in mathematical physics
• Mathematical modeling of complex engineering problems using fractional differential equations
• Advanced analytical methods for fractional differential equations
• Theoretical, computational, and experimental nature of various physical or natural phenomena involving fractional differential equations
• Lie symmetry for fractional nonlinear partial differential equations