Fractional Calculus and Models in Finance and Economics

Dear Colleagues,

Since its initial interest, dating back to the celebrated contributions of mathematicians such as Cauchy, Leibniz, Liouville, and many others, fractional calculus has emerged as a powerful tool in various scientific disciplines. After centuries of relative obscurity, it finally gained substantial attention in the latter half of the 20th century. Today, demonstrating the great versatility of fractional models, it has become a cornerstone in fields ranging from physics to data analysis, from engineering to economics and finance. One of the peculiarities of fractional calculus resides in its ability to model behaviors with long-range dependencies, memory effects, and non-local interactions, which are often prevalent in real-world systems. Unlike classical models that assume instantaneous reactions, fractional calculus-based models allow for the incorporation of past information over an extended period, enabling a more accurate representation of the complex dynamics where the memory of past events or behaviors can significantly influence future outcomes. The inclusion of fractional derivatives in stochastic models, such as the fractional Brownian motion, provides a more realistic representation of irregularities and self-similarity observed in various natural and social phenomena. This has implications not only in physics and engineering but also in understanding the inherent uncertainties and fluctuations in financial markets. As a further generalization, multifractional processes, which involve a combination of different fractional orders, have proven particularly useful in capturing more complex scaling behaviors in various signals, opening avenues for enhanced signal processing techniques.

This Special Issue of Mathematics aims to encourage researchers to submit high-quality papers delving into innovative applications of fractional calculus and related models for a deeper comprehension and prediction of economic and financial phenomena. Topics of interest include fractional and multifractional models, fractional stochastic volatility, scaling and self-similarity, and long memory.

Prof. Dr. Sergio Bianchi
Dr. Massimiliano Frezza
Guest Editors

Manuscript Submission Information

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

• fractional calculus
• fractional differential equations
• fractional and multifractional stochastic processes
• long memory
• scaling
• self-similarity
• non-integer order dynamics
• memory effects
• non-local interactions
• time-varying regularity
• stochastic volatility
• anomalous diffusion
• power-law behavior
• complex systems modeling
• applications in finance and economics