Fractional Calculus and Its Applications: Symmetry and Topics

Dear Colleagues,

Fractional calculus has a reputable history of 325 years of study; however, there are still tremendous problems in this field, from both theoretical and applied viewpoints. Upon its inception, it was not well known and had to be integrated into all of the other applied sciences. The novelty of fractional calculus is that non-integer-order differentiation and integration have global characteristics. Therefore, this discipline describes the history and non-local distribution properties of entities, has an extra degree of freedom, and hence explains natural phenomena better. Consequently, to make this area of study applicable as a popular tool among science and engineering domains with additional dimensions of fractional derivatives and integrals, and to understand nature, the subject of fractional calculus is highly valuable. Since the eighteenth century, this field has only been associated with mathematicians, but in recent decades, it has been addressed in many fields such as engineering, science, and economics. Furthermore, many problems based on continuous data are not explained by the integer-order derivative and have been analyzed by the arbitrary-order derivative; therefore, fractional calculus is superior to integer-order calculus. Ordinary derivatives are thus a part of fractional differential and integral calculus, and this part includes the history of fractional calculus.

This Special Issue of Symmetry will focus on various problems of integer orders that have been investigated in different research articles which only describe the discrete behaviors of the given quantity and cannot deal with non-integer orders. Therefore, to study the continuous spectrum of problems for the dynamics of different systems, fractional calculus has been introduced in the form of differential, integral equations and in the implementation of symmetric or asymmetric processes. Because of the applicability of fractional differential and integral equations, several scholars are very interested in this field to help the, study and explore different mathematical models. This Special Issue will cover topics including, but not limited to, the following:

• Theoretical aspects of fractional differential equations.
• Numerical methods and computational techniques for solving fractional differential equations.
• New analyses of symmetric numerical schemes.
• Fractional differential equations in physics, biology, finance, and engineering.
• Theoretical advancements in the application of fractional differential equations in machine learning.
• Existence, uniqueness, and stability results for solutions of fractional differential equations.
• Fractional differential equations in optimization and machine learning.
• Solving differential equations via artificial neural networks.
• Fractional-order differential and integral equations and systems.
• Nonlinear dynamics and complex systems.
• Fractal and fractional calculus.

Dr. Mati ur Rahman
Prof. Dr. Fuzhang Wang
Guest Editors

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• Fractional differential equations
• Mathematical modeling
• Fixed-point theory
• Fractional operator
• Numerical methods
• Symmetry
• Complex dynamic systems
• New numerical and analytic methods
• Integral transforms
• Fractional calculus with AI applications