Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
6.0
3.3
Journals
Fractal Fract
Special Issues
Advances in Fractional Operators: Mathematical Perspectives and Multidisciplinary Applications
share announcement

Advances in Fractional Operators: Mathematical Perspectives and Multidisciplinary Applications

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

Deadline for manuscript submissions: 25 August 2025 | Viewed by 1424

Special Issue Editors

Dr. Leandro Tavares

E-Mail Website1 Website2
Guest Editor
Center for Mathematics, Computation and Cognition, Federal University of ABC, Santo André 09280-560, SP, Brazil
Interests: partial differential equations; mathematical analysis; equations with fractional operators
Special Issues, Collections and Topics in MDPI journals
Dr. J. Vanterler Da C. Sousa

E-Mail Website
Guest Editor
Department of Mathematics, Aerospace Engineering, PPGEA-UEMA, DEMATI-UEMA, São Luís 65054, Brazil
Interests: fractional differential equations; functional analysis; variational approach; frac-tional calculus; analysis mathematics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

 In the last decade, there has been increasing interest in the study of problems involving fractional operators and their qualitative aspects, potentially due to the possibility of their application in several areas of science such as optimization, finance, phase transitions, stratified materials, anomalous diffusion, crystal dislocation, soft thin films, semipermeable membranes, flame propagation, conservation laws, ultra-relativistic limits of quantum mechanics, quasi-geostrophic flows, multiple scattering, minimal surfaces, materials science, water waves, chemical reactions of liquids, population dynamics, and geophysical fluid dynamics. Moreover, there is significant interest from a mathematical perspective due to the numerous advantages of the fractional setting compared to the traditional one.

Researchers focusing on problems involving fractional operators and their applications are encouraged to submit their original, high-quality work to this Special Issue, which aims to foster innovation and achieve breakthroughs in the study of problems involving fractional operators, tackling both real-world challenges and abstract mathematical issues.

Dr. Leandro Tavares
Dr. J. Vanterler Da C. Sousa
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 equations
  • fractional operators
  • critical point theory
  • variational methods
  • fractional derivatives
  • Ψ-Hilfer fractional derivative
  • Mittag-Leffler function
  • generalized Mittag-Leffler function

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.

Further information on MDPI's Special Issue policies can be found here.

Published Papers (4 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

18 pages, 319 KiB  
Article
On the Existence of Solutions and Ulam-Type Stability for a Nonlinear ψ-Hilfer Fractional-Order Delay Integro-Differential Equation
by Cemil Tunç, Fehaid Salem Alshammari and Fahir Talay Akyıldız
Fractal Fract. 2025, 9(7), 409; https://doi.org/10.3390/fractalfract9070409 - 24 Jun 2025
Viewed by 160
Abstract
In this work, we address a nonlinear ψ-Hilfer fractional-order Volterra integro-differential equation that incorporates n-multiple-variable time delays. Employing the ψ-Hilfer fractional derivative operator, we investigate the existence of a unique solution, as well as the Ulam–Hyers–Rassias stability, semi-Ulam–Hyers–Rassias stability, and [...] Read more.
In this work, we address a nonlinear ψ-Hilfer fractional-order Volterra integro-differential equation that incorporates n-multiple-variable time delays. Employing the ψ-Hilfer fractional derivative operator, we investigate the existence of a unique solution, as well as the Ulam–Hyers–Rassias stability, semi-Ulam–Hyers–Rassias stability, and Ulam–Hyers stability of the proposed ψ-Hilfer fractional-order Volterra integro-differential equation through the fixed-point approach. In this study, we enhance and generalize existing results in the literature on ψ-Hilfer fractional-order Volterra integro-differential equations, both including and excluding single delay, by establishing new findings for nonlinear ψ-Hilfer fractional-order Volterra integro-differential equations involving n-multiple-variable time delays. This study provides novel theoretical insights that deepen the qualitative understanding of fractional calculus. Full article
(This article belongs to the Special Issue Advances in Fractional Operators: Mathematical Perspectives and Multidisciplinary Applications)
28 pages, 531 KiB  
Article
Representation Formulas and Stability Analysis for Hilfer–Hadamard Proportional Fractional Differential Equations
by Safoura Rezaei Aderyani, Reza Saadati and Donal O’Regan
Fractal Fract. 2025, 9(6), 359; https://doi.org/10.3390/fractalfract9060359 - 29 May 2025
Viewed by 354
Abstract
This paper introduces a novel version of the Gronwall inequality specifically related to the Hilfer–Hadamard proportional fractional derivative. By utilizing Picard’s method of successive approximations along with the definition of Mittag–Leffler functions, we derive a representation formula for the solution of the Hilfer–Hadamard [...] Read more.
This paper introduces a novel version of the Gronwall inequality specifically related to the Hilfer–Hadamard proportional fractional derivative. By utilizing Picard’s method of successive approximations along with the definition of Mittag–Leffler functions, we derive a representation formula for the solution of the Hilfer–Hadamard proportional fractional differential equation featuring constant coefficients, expressed in the form of the Mittag–Leffler kernel. We establish the uniqueness of the solution through the application of Banach’s fixed-point theorem, leveraging several properties of the Mittag–Leffler kernel. The current study outlines optimal stability, a new Ulam-type concept based on classical special functions. It aims to improve approximation accuracy by optimizing perturbation stability, offering flexible solutions to various fractional systems. While existing Ulam stability concepts have gained interest, extending and optimizing them for control and stability analysis in science and engineering remains a new challenge. The proposed approach not only encompasses previous ideas but also emphasizes the enhancement and optimization of model stability. The numerical results, presented in tables and charts, are provided in the application section to facilitate a better understanding. Full article
(This article belongs to the Special Issue Advances in Fractional Operators: Mathematical Perspectives and Multidisciplinary Applications)
►▼ Show Figures

Figure 1

18 pages, 327 KiB  
Article
The Strict Stability of Impulsive Differential Equations with a Caputo Fractional Derivative with Respect to Other Functions
by Ravi P. Agarwal, Snezhana Hristova and Donal O’Regan
Fractal Fract. 2025, 9(6), 341; https://doi.org/10.3390/fractalfract9060341 - 26 May 2025
Viewed by 293
Abstract
The aim of this paper is to study a nonlinear system of impulsive fractional differential equations and Caputo fractional derivatives with respect to another function (CFF). The main characteristics of these fractional derivatives are two-fold: first, the lower limit of CFF equals the [...] Read more.
The aim of this paper is to study a nonlinear system of impulsive fractional differential equations and Caputo fractional derivatives with respect to another function (CFF). The main characteristics of these fractional derivatives are two-fold: first, the lower limit of CFF equals the impulsive time of the considered interval; second, the applied function in CFF is changeable at each interval without impulses. An auxiliary system of two linear scalar impulsive fractional differential equations with CFF is considered, and strict stability in a couple is defined. The behavior of its solutions is illustrated with several examples. Also, we use appropriate Lyapunov functions to obtain sufficient conditions for the strict stability of the studied system. These sufficient conditions depend significantly on the type of impulsive function. Full article
(This article belongs to the Special Issue Advances in Fractional Operators: Mathematical Perspectives and Multidisciplinary Applications)
10 pages, 266 KiB  
Article
Ulam–Hyers–Rassias Stability of ψ-Hilfer Volterra Integro-Differential Equations of Fractional Order Containing Multiple Variable Delays
by John R. Graef, Osman Tunç and Cemil Tunç
Fractal Fract. 2025, 9(5), 304; https://doi.org/10.3390/fractalfract9050304 - 6 May 2025
Cited by 1 | Viewed by 382
Abstract
The authors consider a nonlinear ψ-Hilfer fractional-order Volterra integro-differential equation (ψ-Hilfer FrOVIDE) that incorporates N-multiple variable time delays into the equation. By utilizing the ψ-Hilfer fractional derivative, they investigate the Ulam–Hyers–Rassias and Ulam–Hyers stability of the equation by [...] Read more.
The authors consider a nonlinear ψ-Hilfer fractional-order Volterra integro-differential equation (ψ-Hilfer FrOVIDE) that incorporates N-multiple variable time delays into the equation. By utilizing the ψ-Hilfer fractional derivative, they investigate the Ulam–Hyers–Rassias and Ulam–Hyers stability of the equation by using fixed-point methods. Their results improve existing ones both with and without delays by extending them to nonlinear ψ-Hilfer FrOVIDEs that incorporate N-multiple variable time delays. Full article
(This article belongs to the Special Issue Advances in Fractional Operators: Mathematical Perspectives and Multidisciplinary Applications)
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-4
Back to TopTop