Manuscript Topics

Fractional calculus, with all its different cases and interpretations, has been applied by many researchers on problems related to all branches of the sciences. In this field, on the one hand, there is a sizeable community working on real-world applications, and on the other hand, there is a community of mathematicians dealing with theoretical and pure aspects. Both viewpoints are necessary to develop and understand the nature and behaviour of fractional calculus, and each one is an unavoidable complement to the other.

One of the main topics in this area is the study of differential and integral equations using fractional derivatives and integrals. These studies have led to the development of analytical methods for finding explicit solutions, numerical methods for approximating solutions, fixed point methods for proving the existence and/or uniqueness of solutions, qualitative methods for establishing the behaviour of solutions, etc.

Many mathematical techniques for such equations are based on selecting a classical method for differential equations and considering how it may be extended if the operators are permitted to be fractional. Other approaches rely fundamentally on the fractional nature of the operators used. Developing and applying different methods for solving fractional differential equations is a topic of fundamental importance in understanding all the nonlocal and intermediate processes where fractional differential equations are used.

A mathematical understanding of fractional-calculus operators and their behaviours is essential for solving the real problems involving these operators. Applications can be found in the field of mathematics itself and also, for instance, in epidemiology to describe the spread of disease, in bioengineering to model viscoelastic substances, in medicine to describe the movement of drugs through the body, in network problems featuring nonlocal connections, in population dynamical systems, etc.

The goal of this Special Issue is to gather high-level research papers on a selection of different branches of the study of fractional calculus and its applications. We are interested in topics including but not limited to the following:
• Fractional integro-differential equations (of any type) and their generalisations.
• Methodologies for solving fractional differential equations.
• Applications of fractional calculus to real-world problems.
• Harmonic analysis with fractional calculus.
• Obstacle problem with fractional calculus.
• Theoretical investigations of the nature and/or applications of fractional calculus.

Keywords  
Fractional differential equations, integro-differential equations, partial differential equations, operators of fractional calculus, analytical solution methods, numerical and approximation methods, qualitative theory of differential equations, applications of fractional calculus, fractional dynamical systems, harmonic analysis, theory of fractional operators.

For Instructions for authors, please visit
https://www.aimspress.com/era/news/solo-detail/instructionsforauthors
Please submit your manuscript to online submission system
https://aimspress.jams.pub/