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Fractal Fract
Special Issues
Stability Analysis for Fractional-Order Equations
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Stability Analysis for Fractional-Order Equations

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "General Mathematics, Analysis".

Deadline for manuscript submissions: closed (31 July 2023) | Viewed by 3480

Special Issue Editors

Prof. Dr. Jiafa Xu

E-Mail Website
Guest Editor
School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China
Interests: nonlinear functional analysis; fractional differential (difference) equations; fixed point theory; variational methods; iterative methods
Dr. Akbar Zada

E-Mail Website
Guest Editor
Department of Mathematics, University of Peshawar, Peshawar, Pakistan
Interests: nonlinear functional analysis; fractional differential equations; fixed point theory; stability analysis
Special Issues, Collections and Topics in MDPI journals
Dr. Yaohong Li

E-Mail Website
Guest Editor
School of Mathematics and Statistics, Suzhou University, Suzhou 234000, China
Interests: nonlinear functional analysis; fractional differential (difference) equations; fixed point theory; iterative methods

Special Issue Information

Dear Colleagues,

Fractional differential equations (FDEs) have become one of the most attractive research areas for finding new results. The reason is that FDEs can be used to precisely describe a large number of nonlinear phenomena in different branches of science and engineering, for example, of viscoelasticity, control hypothesis, speculation, fluid dynamics, hydrodynamics, and aerodynamics in information processing, system networking, and picture processing. They are also a useful instrument for the depiction of memory and inherited properties of numerous materials and processes. As a result, FDE theory has undergone significant developments in recent years. In the study of DEs, stability analysis is a basic requirement for the applicability of results. This is especially the case in stability theory, particularly regarding Ulam's stability, which was first established by Ulam and extended by Hyers to DEs and plays a pivot role. However, we note that with respect to stability analysis in FDEs, there still are many problems that need to be studied. In this Special Issue “Stability Analysis for Fractional-Order Equations”, we aim to create new theories and applications for stability analysis in FDEs. We welcome original research articles.

Keywords (include but are not limited to the following):

  • Fractional differential equations;
  • Existence of solutions for FDEs;
  • Exact and numerical solutions for FDEs;
  • Stability analysis for FDEs.

Prof. Dr. Jiafa Xu
Dr. Akbar Zada
Dr. Yaohong Li
Guest Editors

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.

Keywords

  • fractional differential equations
  • existence of solutions for FDEs
  • exact and numerical solutions for FDEs
  • stability analysis for FDEs

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Published Papers (2 papers)

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Research

14 pages, 379 KiB  
Article
Local Stability, Global Stability, and Simulations in a Fractional Discrete Glycolysis Reaction–Diffusion Model
by Tareq Hamadneh, Amel Hioual, Omar Alsayyed, Yazan Alaya AL-Khassawneh, Abdallah Al-Husban and Adel Ouannas
Fractal Fract. 2023, 7(8), 587; https://doi.org/10.3390/fractalfract7080587 - 29 Jul 2023
Cited by 8 | Viewed by 1647
Abstract
In the last few years, reaction–diffusion models associated with discrete fractional calculus have risen in prominence in scientific fields, not just due to the requirement for numerical simulation but also due to the described biological phenomena. This work investigates a discrete equivalent of [...] Read more.
In the last few years, reaction–diffusion models associated with discrete fractional calculus have risen in prominence in scientific fields, not just due to the requirement for numerical simulation but also due to the described biological phenomena. This work investigates a discrete equivalent of the fractional reaction–diffusion glycolysis model. The discrete fractional calculus tool is introduced to the discrete modeling of diffusion problems in the Caputo-like delta sense, and a fractional discretization diffusion model is described. The local stability of the equilibrium points in the proposed discrete system is examined. We additionally investigate the global stability of the equilibrium point by developing a Lyapunov function. Furthermore, this study indicates that the L1 finite difference scheme and the second-order central difference scheme can successfully preserve the characteristics of the associated continuous system. Finally, an equivalent summation representing the model’s numerical formula is shown. The diffusion concentration is further investigated for different fractional orders, and examples with simulations are presented to corroborate the theoretical findings. Full article
(This article belongs to the Special Issue Stability Analysis for Fractional-Order Equations)
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15 pages, 321 KiB  
Article
Lyapunov-Type Inequalities for Systems of Riemann-Liouville Fractional Differential Equations with Multi-Point Coupled Boundary Conditions
by Yumei Zou and Yujun Cui
Fractal Fract. 2023, 7(6), 454; https://doi.org/10.3390/fractalfract7060454 - 1 Jun 2023
Cited by 1 | Viewed by 948
Abstract
We consider a system of Riemann–Liouville fractional differential equations with multi-point coupled boundary conditions. Using some techniques from matrix analysis and the properties of the integral operator defined on two Banach spaces, we establish some Lyapunov-type inequalities for the problem considered. Moreover, the [...] Read more.
We consider a system of Riemann–Liouville fractional differential equations with multi-point coupled boundary conditions. Using some techniques from matrix analysis and the properties of the integral operator defined on two Banach spaces, we establish some Lyapunov-type inequalities for the problem considered. Moreover, the comparison between two Lyapunov-type inequalities is given under certain special conditions. The inequalities obtained compliment the existing results in the literature. Full article
(This article belongs to the Special Issue Stability Analysis for Fractional-Order Equations)
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