Numerical Models and Approximation Techniques in Fractional Calculus

Dear Colleagues,

Fractional calculus has witnessed a tremendous impulse in recent years given all its potential applications in the sciences and engineering. New fractional derivatives have been introduced as a means to provide more accurate descriptions of real-life phenomena or as interesting generalizations of integer-order calculus. In any case, the results obtained have contributed to enrichen current mathematical theories, and a better understanding of some physical phenomena has been obtained along the way. This development has been vertiginous, and it is easy to lose track of all the recent progress in this area. As a way to alleviate this problem, the present Special Issue intends to be a platform to disseminate the most important results obtained recently in this area. More precisely, the aim is to showcase the most relevant new results in numerical analysis and approximation techniques to solve problems involving fractional-order operators. The computational and numerical resolution of mathematical models described by deterministic and stochastic integral and/or differential equations of fractional order are of particular interest in this Special Issue. Analytical approximation techniques to estimate the solutions of fractional differential equations are certainly topics of interest. The design of numerical models to approximate such models and the theoretical analysis of those techniques are also relevant. Particularly, we encourage the submission of manuscripts that investigate the consistency, stability, and convergence of numerical models for fractional partial differential equations. We welcome reports which thoroughly investigate the physical properties of fractional-order systems through analytical tools or simulations. Potential applications of fractional calculus are also welcome, with the understanding that sufficient physical reasons are provided to use fractional-order operators. Moreover, we welcome works in which artificial intelligence is employed to solve complex phenomena involving fractional operators. All the papers published in this Special Issue will be high-quality articles that advance our understanding and analysis of fractional-order systems in the sciences and engineering.

Prof. Dr. Jorge E. Macías Díaz
Guest Editor

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• numerical models
• numerical analysis
• approximation techniques
• fractional-order systems
• mathematical analysis