Recent Trends in Fractional Integral and Derivative Operators

Dear Colleagues,

The behavior of numerous dynamic systems, including diffusion processes, milling processes, data networks, transportation, plasma physics, Lévy processes, economics, flexible structures, and continuum robots, is often effectively described using fractional operators. Operators like fractional derivatives and integrals are essential for capturing the complex dynamics and memory effects in these systems. Fractional-order models are particularly useful for systems with long-term memory, hereditary effects, and nonlocal interactions, providing a more accurate description than traditional local models.

We are pleased to announce a Special Issue titled “Recent Trends in Fractional Integral and Derivative Operators”, which aims to highlight the latest developments, methodologies, and applications of fractional calculus in control theory and the modeling of dynamical systems. This Special Issue provides a platform for researchers to explore and discuss developments in the use of fractional integrals and derivatives across a wide range of systems.

We invite original research articles and reviews that explore various aspects of fractional-order systems, including but not limited to, the following research areas:

• Fractional-order systems and their theoretical foundations.
• Applications of fractional derivatives in diffusion and random walk processes.
• Time-delay systems involving fractional integrals and derivatives.
• Fractional calculus in control theory, including modeling and stability analysis.
• Stochastic systems and Lévy processes modeled with fractional operators.
• Numerical methods for solving fractional differential equations.
• The role of fractional operators in modeling physical and engineering systems.

We encourage your contributions to this Special Issue, which will advance the understanding and application of fractional calculus across various scientific and engineering fields. Your work will be pivotal in shaping the future of fractional-order systems and their practical implementations.

Dr. Arman Dabiri
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 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.

• time-delay systems
• control theory for continuum systems
• fractional-order systems
• fractals and chaos
• Volterra integro-differential systems
• stochastic systems
• diffusion and random walk processes
• non-Markov processes
• computational methods for nonlocal operators

• Advances in Fractional Integral and Derivative Operators with Applications in Fractal and Fractional (16 articles)