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Recent Trends in the Computational and Mathematical Methods of Fractional Calculus

Guest Editors:

Jorge E. Macías-Díaz

Tallinn University, Estonia

Universidad Autónoma de Aguascalientes, Mexico

jemacias@correo.uaa.mx

Dumitru Baleanu

Cankaya University, Turkey

dumitru@cankaya.edu.tr

Proposal:

The theory of fractional-order integro-differential operators (fractional calculus, for short) has been one of those areas in mathematics which has undergone a tremendous development in the last decades. Indeed, various fractional derivatives have been introduced in the literature to extend the traditional calculus and to provide more accurate descriptions of processes in physics, chemistry and biology. From the analytic point of view, the theory of fractional-order integro-differential operators has contributed decisively to the development of other areas in mathematics, including ordinary and partial differential equations, numerical analysis, calculus of variations, optimization theory. From a more pragmatic point of view, some important applications of fractional calculus have been found in physics, biology, chemistry and engineering, and new applications are frequently proposed to other areas of the sciences and to the development of new technology. Needless to mention that the speed at which this area expands is vertiginous.

The purpose of this special issue is to provide a means to communicate recent progresses in the field of fractional-order integro-differential operators. We invite researchers in this area to submit high-quality papers which stress the development of new computational and mathematical methods in fractional calculus. Applications of those methods to the analysis of the existence, uniqueness and regularity of the solutions of systems consisting of fractional integro-differential equations is an important topic considered in this work. The development and rigorous analysis of numerical methods to approximate solutions of systems of fractional-order equations is also a relevant topic in this special issue. Among others, optimization problems where the objective or the constraints are described in terms of fractional derivatives, the derivations of exact analytic solutions of systems of partial integro-differential equations, the determination of new conservation laws of these system, are all topics which are considered in this work. Likewise, the application of fractional calculus to modern problems in the sciences and engineering are problems which are covered in this special issue.

The potential topics include, but are not limited to:

Fractrional-order integro-differential operator theory.

Analysis of the solutions of integro-differential systems.

Development of new fractional integrals and derivatives, and their properties.

Special solutions of fractional-order systems.

Mathematical modeling through fractional integrals and derivatives.

Fractional-order variational calculus.

Numerical methods for integro-differential equations.

Stability and convergence analysis of methods for integro-difrerential equations.

Applications to the sciences and engineering.

Submission Details:

Authors should obey with the instructions for authors and quality requirements of CMM. All

papers must be submitted via the online system



Authors need to make sure that they specify the paper is a contribution for ‘‘Special Issue on Recent Trends in the Computational and Mathematical Methods in Fractional Calculus" and select the article type, when prompted, SI: . All papers will be peer reviewed according to the high standards of CMM.

Important Dates:

Deadline of Submission: 31.05.2021

Author Notification: 31.07.2021

Deadline for Revised Papers: 31.10.2021

Final Acceptance: 01.01.2022

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