The subject of fractional calculus based on integrals and derivatives of fractional order has attracted the attention of researchers from many fields of science, especially mathematicians. It has various applications in diverse and widespread fields of engineering and science such as electromagnetics, quantum mechanics, plasma physics, fluid mechanics, chemical physics, mathematical biology, biomedicine, financial systems, chaos, elasticity, control, optics, signals processing, and more. This is a clear indication that fractional calculus is of great importance in modeling real-life problems and obtaining mathematical solutions for these models.

Since mathematical problems encountered in real life are usually modeled with differential equations, it is very important to obtain numerical, analytical, and exact solutions of fractional differential equations, and many mathematical methods have been developed in the literature for this. On the other hand, a new perspective on fractional calculus has been presented by using the concepts of multiplicative, fuzzy fractional derivatives, and integral. New approaches on fractional calculus theory and applications are carried out in the light of scientific studies on these subjects.

This Special Issue aims to create new theories and applications on subjects such as fractional calculus, multiplicative fractional calculus, and fuzzy fractional calculus. It also aims to develop and apply new methods for analytical, numerical, and exact solutions to physical problems in various fields of science. We welcome original research and review articles.

Potential topics include but are not limited to the following:

• New definitions and applications in fractional calculus
• Special functions in fractional calculus
• Applications of fractional calculus in nonlinear science
• Fractional calculus models in physics, biology, medicine, engineering, etc.
• Chaos and dynamical systems related to fractional calculus
• Fractional differential equation and its applications
• Numerical methods for fractional differential equations
• Solitary wave solutions in mathematical physics
• Multiplicative fractional calculus and its applications
• Fuzzy fractional calculus and its applications