Fractional Calculus: Methods and Modeling in Physics, Engineering and Applied Sciences — in Memory of Prof. J. A. Tenreiro Machado

In Memory of Prof. J. A. Tenreiro Machado

On October 6, 2021 Prof. Tenreiro Machado passed away. We dedicate this Special Issue to his memory. We are not able to express our sadness for this loss. He was a pioneer in the field of fractional calculus. The breadth of Prof. Tenreiro Machado’s research, the global dissemination of his results, and his legacy belong to all scholars involved in any way in the study of fractional calculus. In particular, Professor Hammouch remembers that Prof. Tenreiro Machado was a deeply passionate scholar. His sense of humor was a gift to all those who knew him. We are proud that he was the Editor-in-Chief of Mathematics when this Special Issue was proposed.

Dear Colleagues,

During the last four decades, fractional calculus has been found to be remarkably popular and important, due mainly to their demonstrated applications in numerous seemingly diverse and widespread fields of mathematics, physics, engineering, etc. In particular, it extends the classical problems based on differential models. This allows us to generalize several mathematical models often described by derivatives of integer order (e.g., fractal media). Nevertheless, in current literature, there are several definitions of fractional derivative (Riemann–Liouville, Grünwald–Letnikov, etc.). Accordingly, many researchers work on overcoming this difficulty in order to get a unique definition of fractional derivative.

This would shed new light on the fractional calculus. Moreover, fractional calculus provides several tools for solving differential, integral, integro-differential equations and nonlinear models in mathematical physics. In the last ten years, considerable attention has been paid to fractional calculus in the complex plane. Several publications have appeared documenting the aforementioned interest, especially about the class of holomorphic functions.

Consequently, the fractional calculus of special functions represents one of the most interesting research topics in contemporary mathematics. As a result, the link between fractional calculus and other mathematical fields may provide new results and applications by opening up new frontiers in research. This is the case of the concept of symmetry, as shown by its recent applications in the concept of symmetry (e.g., Lie symmetry analysis of fractional PDEs, fractional supersymmetric quantum mechanics). Fractional calculus is nowadays applied in several fields of science, such as quantum mechanics, information theory, dynamical systems and health science. Moreover, many researchers have also found applications in non-scientific areas (e.g., life sciences, social sciences).

In this Special Issue, we invite and welcome review, expository and original papers dealing with recent advances in fractional calculus and from a more general point of view to all theoretical and practical studies in mathematics, physics and engineering focused in some way on this topic.

The main topics of this Special Issue include (but are not limited to):

• Fractional equations;
• Fractional modelling;
• Fractional calculus of special functions;
• Entropy concept and fractional calculus;
• Fractional boundary value problems;
• Fractional control theory;
• Chaoticity and fractional calculus;
• Fractal geometry and fractional calculus;
• Fractional differential equations;
• Integral boundary conditions;
• Banach contraction principle;
• Dynamical systems;
• Fractional-order systems;
• Delay differential equations;
• Mathematical modelling;
• Numerical methods;
• Neural networks;
• Optimization;
• Control systems.

Dr. Emanuel Guariglia
Prof. Dr. Seenith Sivasundaram
Guest Editors

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• fractional derivative
• fractional operator
• symmetry
• fractal media
• chaoticity
• special functions
• control theory
• dynamical systems