In recent years, fractional analysis has become a field of study that has increased in popularity because of its effective application in different scientific fields such as statistics, applied mathematics, dynamics, mathematical biology, control theory, optimisation, and chaos theory. Fractional analysis continues to rapidly develop with the definition of new derivative, and integral operators.

Identifying new operators has become a topic extensively addressed by many researchers, who research new features, and real-life applications of new operators in applied mathematics, engineering, and mathematical biology. For instance, new operators have started being used in inequality theory. Some of the new integral, and derivative operators differ from others; while the locality and singularity options differ from others, and while others have become primarily investigated with the derivative of the order of zero. Besides the characteristics of each new operator, what makes an operator different and effective is also a research area open to discussion. In recent years, many studies have been focussing on fractional calculus addressing real-world problems. Moreover, research on fractional ordinary or partial differential equations and other relevant topics relating to the integer order model has attracted the attention of experts worldwide. New fractional derivatives, and integral operators have become some of the most effective tools in contributing to the physical phenomena. They are also useful as applications to real-world problems.

The aim of this Special Issue is to solicit original research articles, as well as review articles, focussing on the application of fractional calculus to real-world problems. This Special Issue hopes to establish an online discussion platform for researchers from varied scientific fields (physics, biology, chemistry, economics, medicine, and engineering). We also wish that this Special Issue becomes a platform for inspiring ideas, and new results in fractional calculus.

Potential topics include but are not limited to the following:

• Generalised fractional calculus, and applications
• Fractional differential equations
• Discrete fractional equations
• Novel fractional calculus definitions, their properties, and applications
• Fractional calculus models in physics, biology, chemistry, economics, medicine, and engineering
• Numerical methods for fractional differential equations
• Optimisation problems
• Fractional derivatives, and special functions
• Various special functions related to generalised fractional calculus
• Special functions related to fractional non-integer order control systems, and equations
• Special functions arising in the fractional diffusion-wave equations
• Operational methods in fractional calculus
• Fractional integral inequalities, and their q-analogues
• Inequalities involving the fractional integral operators
• Applications of inequalities for classical, and fractional differential equations