|| Special Issue || Advancements in Fractional Calculus: Theoretical and Experimental Aspects
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Deadline for Submissions: 31 December 2023 |
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Special Issue Editors |
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Guest Editor |
Dr. Pushpendra Kumar |
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Affiliation |
Institute for the Future of Knowledge, University of Johannesburg, PO Box 524, Auckland Park 2006, South Africa |
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Interests |
fractional calculus; mathematical modeling; numerical methods; dynamical systems |
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Guest Editor |
Prof. Dr. Vedat Suat Erturk |
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Affiliation |
Department of Mathematics, Ondokuz Mayis University, Atakum-55200, Samsun, Turkey |
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Special Issue Information |
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* This Special Issue is in cooperation with the International Conference on Fractional Calculus: Theory, Applications and Numerics (ICFCTAN, 27–29 January 2023, National Institute of Technology Puducherry, Karaikal, India). A cover letter must be provided indicating the submission from ICFCTAN.
Nowadays, Fractional calculus or non-integer order calculus is one of the most highlighted research areas of mathematics which deals with the theory and application of integrals and derivatives of arbitrary order. Fractional calculus is applicable to almost all branches of applied sciences such as engineering, mathematical biology, mathematical epidemiology, statistics, dynamics, optimization, control theory, mathematical ecology, psychological problems, plant science, and chaos theory, due to the fascinating memory effects and non-locality. Also, fractional-order analysis is increasing very sharply with the proposals of new derivative and integral operators. A number of new fractional derivatives have been proposed by researchers. Probably, most of the fractional derivative and integral operators differ from others cause of the different properties of each new operator, which makes an operator dynamically unique and emphatic. Unfortunately, the different features of fractional derivatives also bring difficulty in numerical simulations and computational costs. Then the gap was generated from theory to real-world applications. It is challenging work to find new tools to depict discrete memory effects. Very recently, fractional-order operators have been considered a strong simulating and modeling tool for problems in mechanical engineering. A number of physical laws have been simulated more effectively in the sense of fractional differential equations. More than that, there is a very big demand for powerful computational algorithms for simulating fractional-order dynamics in order to derive various optimal control problems.
On the other hand, discrete fractional calculus was also proposed very recently. As we know the memory kernel is expressed by implementing the discrete functions on the time scale and avoids the errors from the numerical discretization. It is particularly suitable for fractional modeling with computer applications. Many roles of fractional dynamics in the neural network, signal processing, time series, and big data become possible now.
In this Special Issue, our main target is to explore the various improvements in the theory and applications of fractional calculus by publishing original and high-quality research and review papers. Here we target to make an online research platform for scientists from different scientific areas. In this matter, we kindly invite scientists to submit their original high-quality works in the field of fractional calculus as models of complex engineering phenomena, epidemic studies, ecological phenomena, and many other real-world problems. These researches may also bring novel theories, new experimental simulations, development of various numerical techniques, and their applications in the sense of fractional-order operators. We hope that this Special Issue will become a perfect platform for inspiring new thoughts, and results in fractional calculus in a theoretical and experimental manner.
The topics to be covered include, but are not limited to: · Fractional differential equations and integral inequalities · New fractional operator definitions, their characteristics, and applications · Implementation of fractional-order dynamical systems in epidemiology, biology, ecology, finance, environmental science, fluid mechanics, signal and image processing, chemistry, physics, electricity, and medicine. · Mathematical models for various complex engineering problems in the sense of fractional-order operators · Tools of artificial intelligence and data analysis by applying fractional numerical techniques · Different analytical and numerical algorithms to solve fractional-order dynamical systems or models; · Stability analysis and control design for fractional-order systems · Fractional optimal control · Discrete fractional equations · New dynamical analysis of fractional discrete-time systems · Optimisation problems · Special functions concerned with fractional-order control problems |
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Published Papers |
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This special issue is now open for submission. |
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