Fractional Calculus and Its Application to Arbitrary Time Scales

A special issue of Fractal and Fractional (ISSN 2504-3110).

Deadline for manuscript submissions: closed (31 July 2021) | Viewed by 2984

Special Issue Editors

Department of Mathematics and Computer Science, Alabama State University, Montgomery, AL 36101, USA
Interests: mathematical inequalities; fractional calculus; time scale theory; growth properties of complex polynomials
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Co-Guest Editor
Department of Mathematics, Computer Science and Information Systems, California University of Pennsylvania, PA 15419, USA
Interests: fractional calculus; numerical analysis and methods; fixed point theory and its applications
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue is devoted to recent developments in the application of fractional calculus to time scales.

In recent years, fractional (non-integer order) calculus has been applied in many fields, such as control theory for dynamical systems, nanotechnology, viscoelasticity, anomalous transport and anomalous diffusion, financial modeling, and random walks. These recent discoveries of the applications of fractional calculus have drawn the attention of many researchers in order to gain further insight into the field, including into the existence and uniqueness of solutions, asymptotic behaviour, and analytical and numerical solutions of some linear and nonlinear fractional differential equations.

In 1988, the theory of time scales was introduced. Ever since then, much work has been done on time scales. Currently, the application of fractional calculus to time scales is a subject of strong interest. It is the purpose of this Special Issue to collate some of the recent developments on this subject.

Dr. Eze R. Nwaeze
Dr. Olaniyi S Iyiola
Guest Editors

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Keywords

  • dynamical systems on a time scale based on fractional calculus
  • time scale operators of fractional calculus and their applications
  • fractional inequalities on time scales
  • fractional differential equations on time scales
  • modeling with fractional derivatives on time scales

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Published Papers (1 paper)

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Research

12 pages, 2800 KiB  
Article
Lipschitz Stability in Time for Riemann–Liouville Fractional Differential Equations
by Snezhana Hristova, Stepan Tersian and Radoslava Terzieva
Fractal Fract. 2021, 5(2), 37; https://doi.org/10.3390/fractalfract5020037 - 21 Apr 2021
Cited by 13 | Viewed by 2227
Abstract
A system of nonlinear fractional differential equations with the Riemann–Liouville fractional derivative is considered. Lipschitz stability in time for the studied equations is defined and studied. This stability is connected with the singularity of the Riemann–Liouville fractional derivative at the initial point. Two [...] Read more.
A system of nonlinear fractional differential equations with the Riemann–Liouville fractional derivative is considered. Lipschitz stability in time for the studied equations is defined and studied. This stability is connected with the singularity of the Riemann–Liouville fractional derivative at the initial point. Two types of derivatives of Lyapunov functions among the studied fractional equations are applied to obtain sufficient conditions for the defined stability property. Some examples illustrate the results. Full article
(This article belongs to the Special Issue Fractional Calculus and Its Application to Arbitrary Time Scales)
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