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Advances in Fractional Calculus for Modeling and Applications
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Advances in Fractional Calculus for Modeling and Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 30 June 2026 | Viewed by 2685

Special Issue Editors

Prof. Dr. Assia Guezane-Lakoud

E-Mail Website
Guest Editor
Department of Mathematics, Badji Mokhtar University, Annaba 23000, Algeria
Interests: fractional differential equation; ordinary differential equation; integral inequalities; qualitative theory of ordinary and fractional differential equations
Prof. Dr. Rabah Khaldi

E-Mail Website
Guest Editor
Department of Mathematics, Badji Mokhtar University, Annaba 23000, Algeria
Interests: fractional differential equation; ordinary differential equation; orthogonal polynomials; approximation theory

Special Issue Information

Dear Colleagues, 

We are pleased to introduce the Special Issue “Advances in Fractional Calculus for Modeling and Applications”. This collection is devoted to recent developments in fractional calculus and its growing significance as a tool for analyzing and modeling complex systems in science and engineering.

Classical integer-order models often encounter difficulties when dealing with processes that involve memory, long-range dependence, or nonlocal dynamics. Fractional calculus, by generalizing differentiation and integration to non-integer orders, offers a more flexible and precise framework to capture such effects. Its ability to represent real-world phenomena with higher fidelity has led to increasing applications in many areas, including physics, biology, medicine, engineering, finance, and even interdisciplinary fields such as geophysics, energy, and social systems.

The scope of this Special Issue includes new results on fractional differential equations, anomalous diffusion and transport, hereditary phenomena, fractional-order control, as well as computational and numerical approaches for simulation. We also encourage submissions that introduce novel analytical techniques, efficient algorithms, and interdisciplinary applications that demonstrate the practical impact of fractional models.

Our goal is to bring together contributions that connect theoretical progress with practical implementations, creating a valuable reference for researchers, while further promoting the use of fractional calculus in addressing contemporary challenges.

We warmly invite you to contribute your latest findings and perspectives to this Special Issue.

Prof. Dr. Assia Guezane-Lakoud
Prof. Dr. Rabah Khaldi
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 250 words) can be sent to the Editorial Office for assessment.

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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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 calculus
  • non-integer order modeling
  • fractional differential equations
  • fractional integral inequalities
  • fractional-order control
  • computational and numerical methods

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Published Papers (6 papers)

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Research

27 pages, 1030 KB  
Article
Study of a Coupled Integral–Multipoint Boundary Value Problem of Langevin–Type Nonlinear Riemann–Liouville and Hadamard Fractional Differential Equations
by Bashir Ahmad, Hafed A. Saeed, Boshra M. Alharbi and Sotiris K. Ntouyas
Mathematics 2026, 14(8), 1280; https://doi.org/10.3390/math14081280 - 12 Apr 2026
Viewed by 260
Abstract
Fractional Langevin models are found to be useful in the study of physical phenomena such as diffusion processes, gait variability, etc. Langevin equations involving different fractional–order operators and boundary conditions have been addressed by many researchers. In this article, we formulate a new [...] Read more.
Fractional Langevin models are found to be useful in the study of physical phenomena such as diffusion processes, gait variability, etc. Langevin equations involving different fractional–order operators and boundary conditions have been addressed by many researchers. In this article, we formulate a new Langevin model consisting of a coupled system of Riemann–Liouville and Hadamard–type nonlinear fractional differential equations and coupled multipoint–integral boundary conditions. We present the existence and Ulam–Hyers stability criteria for solutions of the given model problem. Our study is based on the tools of the fixed–point theory. Numerical examples with graphical representations of solutions are offered to demonstrate the application of the obtained results. Our work is novel and useful in the given configuration, and specializes to some new results. Full article
(This article belongs to the Special Issue Advances in Fractional Calculus for Modeling and Applications)
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38 pages, 417 KB  
Article
On Sequential Coupled Caputo-Type Fractional Differential Inclusions with Coupled Boundary Conditions: A Multivalued Fixed-Point Approach
by Manigandan Murugesan, Saravanan Shanmugam, Sekar Elango, Mohamed Rhaima and Elavarasan Krishnasamy
Mathematics 2026, 14(7), 1193; https://doi.org/10.3390/math14071193 - 2 Apr 2026
Viewed by 295
Abstract
This study addresses the existence of solutions for a class of coupled fractional differential inclusions subject to coupled boundary conditions. The analysis is developed within the framework of nonlinear functional analysis by employing Carathéodory-type assumptions, the Leray–Schauder nonlinear alternative, and the Covitz–Nadler fixed-point [...] Read more.
This study addresses the existence of solutions for a class of coupled fractional differential inclusions subject to coupled boundary conditions. The analysis is developed within the framework of nonlinear functional analysis by employing Carathéodory-type assumptions, the Leray–Schauder nonlinear alternative, and the Covitz–Nadler fixed-point theorem for multivalued mappings. The proposed approach accommodates both convex and non-convex set-valued nonlinearities, thereby broadening the scope of the results. Under suitable restrictions on the problem parameters, several corollaries are established as direct consequences of the main findings. An example is included to demonstrate the practical applicability and validity of the theoretical results. Full article
(This article belongs to the Special Issue Advances in Fractional Calculus for Modeling and Applications)
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18 pages, 278 KB  
Article
Existence and Compactness of the Solution Set for a Coupled Caputo Fractional System with ϕ-Laplacian Operators and Nonlocal Boundary Conditions
by Samia Youcefi, Sandra Pinelas, Osama Oqilat, Mohammed Said Souid and M’hamed Bensaid
Mathematics 2026, 14(7), 1112; https://doi.org/10.3390/math14071112 - 26 Mar 2026
Viewed by 356
Abstract
In this paper, we investigate a class of coupled fractional differential systems involving Caputo derivatives and nonlinear ϕ-Laplacian operators subject to nonlocal boundary conditions. By transforming the problem into an equivalent integral system via appropriate Green’s functions, the existence of solutions is [...] Read more.
In this paper, we investigate a class of coupled fractional differential systems involving Caputo derivatives and nonlinear ϕ-Laplacian operators subject to nonlocal boundary conditions. By transforming the problem into an equivalent integral system via appropriate Green’s functions, the existence of solutions is studied within a generalized Banach space framework. Using a Leray–Schauder type fixed point theorem and suitable growth conditions on the nonlinear terms, we establish the existence of at least one bounded solution. Furthermore, we prove that the solution set is compact. An illustrative example involving the p-Laplacian operator is provided to demonstrate the applicability of the obtained theoretical results. Full article
(This article belongs to the Special Issue Advances in Fractional Calculus for Modeling and Applications)
13 pages, 276 KB  
Article
Existence of Mild Solutions to Impulsive Fractional Equations with Almost-Sectorial Operators
by Mostefa Seghier, Kadda Maazouz and Rosana Rodríguez-López
Mathematics 2025, 13(24), 3999; https://doi.org/10.3390/math13243999 - 15 Dec 2025
Viewed by 418
Abstract
This study investigates the existence of mild solutions to impulsive fractional differential equations involving almost-sectorial operators. Through the application of solution operator techniques, fixed-point theory, and Laplace transform, we demonstrate the existence of a unique mild solution to the considered system. Full article
(This article belongs to the Special Issue Advances in Fractional Calculus for Modeling and Applications)
12 pages, 300 KB  
Article
Existence Theory for a Class of Nonlinear Langevin Fractional (p,q)-Difference Equations in Banach Space
by Mouataz Billah Mesmouli, Loredana Florentina Iambor and Taher S. Hassan
Mathematics 2025, 13(24), 3934; https://doi.org/10.3390/math13243934 - 9 Dec 2025
Viewed by 334
Abstract
This paper is devoted to the study of existence results for a nonlinear Langevin-type fractional (p,q)-difference equation in Banach space. The considered model extends the fractional q-difference Langevin equation by introducing two parameters p and q, [...] Read more.
This paper is devoted to the study of existence results for a nonlinear Langevin-type fractional (p,q)-difference equation in Banach space. The considered model extends the fractional q-difference Langevin equation by introducing two parameters p and q, which provide additional flexibility in describing discrete fractional processes. By using the Kuratowski measure of noncompactness together with Mönch’s fixed-point theorem, we derive sufficient conditions that guarantee the existence of at least one solution. The main idea consists in converting the boundary value problem into an equivalent fractional (p,q)-integral equation and verifying that the corresponding operator is continuous, bounded, and condensing. An illustrative example is presented to demonstrate the applicability of the obtained results. Full article
(This article belongs to the Special Issue Advances in Fractional Calculus for Modeling and Applications)
15 pages, 280 KB  
Article
Controllability of Fractional Integro-Differential Equations with Delays and Singular Kernels in Fréchet Spaces
by Fatima Mesri, Abdelkrim Salim and Mouffak Benchohra
Mathematics 2025, 13(22), 3685; https://doi.org/10.3390/math13223685 - 17 Nov 2025
Cited by 1 | Viewed by 488
Abstract
This paper is devoted to the investigation of existence and approximate controllability results for a class of fractional integro-differential equations formulated in Fréchet spaces. The analysis is carried out using a generalized version of Darbo’s fixed point theorem adapted to Fréchet spaces, combined [...] Read more.
This paper is devoted to the investigation of existence and approximate controllability results for a class of fractional integro-differential equations formulated in Fréchet spaces. The analysis is carried out using a generalized version of Darbo’s fixed point theorem adapted to Fréchet spaces, combined with the concept of the measure of noncompactness. To demonstrate the validity and applicability of the theoretical findings, an illustrative example is presented to demonstrate the applicability and validity of the theoretical findings. Full article
(This article belongs to the Special Issue Advances in Fractional Calculus for Modeling and Applications)
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