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Axioms
Special Issues
Numerical Analysis, Approximation Theory and Related Topics
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Numerical Analysis, Approximation Theory and Related Topics

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 30 November 2026 | Viewed by 2428

Special Issue Editors

Dr. Rada Mutavdžić Đukić

E-Mail Website
Guest Editor
Department of Mathematics, Faculty of Mechanical Engineering, University of Belgrade, 11000 Belgrade, Serbia
Interests: numerical integration; numerical methods for integral equations; numerical linear algebra; interpolation in complex plane; approximation theory
Prof. Dr. Gradimir V. Milovanović

E-Mail Website
Guest Editor
Mathematical Institute, Serbian Academy of Sciences and Arts, 11000 Belgrade, Serbia
Interests: approximation theory; special functions; extremal problems; inequalities; orthogonal polynomials; nonclassical orthogonal polynomials; numerical analysis; numerical linear algebra; interpolation in complex plane; orthogonality on the semicircle
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The aim of this Special Issue is to bring together the most recent developments in different fields of numerical analysis and approximation theory as well as applied mathematics in a broader sense and other related topics. This Special Issue will focus on, but is not limited to, the following list of topics:

Manuscripts on numerical integration, numerical methods for differential and integral equations, numerical linear algebra and inverse problems, computational algorithms, computational complexity, imaging and data processing, data approximation, and applications, mathematical modeling, dynamical systems, classical approximation, statistical and fuzzy approximation, approximation in the complex plane, approximation methods for functional equations, best approximation, linear and nonlinear approximation, multivariate approximation, rational approximation, interpolation, splines, orthogonal polynomials, general orthogonal systems, generating functions, special orthogonal functions, special polynomials, special functions in mathematical physics, hypergeometric functions, Fourier series, q-calculus, umbral calculus, numerical approximation, optimization methods and applications, and other related topics and applications thereof are welcome for submission.

We hope that this initiative will be attractive to experts in approximation theory, numerical analysis, and special functions. We encourage you to submit your current research to be included in this Special Issue.

Dr. Rada Mutavdžić Đukić
Prof. Dr. Gradimir V. Milovanović
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. Axioms 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 2400 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

  • numerical analysis
  • numerical linear algebra
  • special functions
  • approximation theory
  • applied mathematics

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Published Papers (3 papers)

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Research

26 pages, 397 KB  
Article
Qualitative Analysis of Uncertain Fractional Differential Equations and Application to Interest Rate Modeling
by Muhammad Imran Liaqat and Abdulaziz Khalid Alsharidi
Axioms 2026, 15(5), 316; https://doi.org/10.3390/axioms15050316 - 28 Apr 2026
Viewed by 196
Abstract
Uncertain fractional differential equations model complex systems that exhibit memory effects and are influenced by human-based uncertainty. These equations provide a flexible and accurate framework for representing real-world phenomena, particularly in situations where traditional probabilistic methods are inadequate, such as modeling financial market [...] Read more.
Uncertain fractional differential equations model complex systems that exhibit memory effects and are influenced by human-based uncertainty. These equations provide a flexible and accurate framework for representing real-world phenomena, particularly in situations where traditional probabilistic methods are inadequate, such as modeling financial market systems where uncertainty and memory effects play a significant role. This research first presents an existence and uniqueness result for the uncertain fractional system with the φ-Hilfer fractional derivative, obtained via the successive approximation approach. Then the analytical solution is derived using the Mittag–Leffler function, and sample continuity is demonstrated under Lipschitz and linear growth conditions. To illustrate the applicability of the theory, we consider an interest rate model and provide two numerical examples to support the theoretical results on existence and uniqueness. All results are developed using the φ-Hilfer fractional derivative, which generalizes the Caputo, Hadamard, and Katugampola fractional derivatives. Consequently, the results are presented in a generalized form. Full article
(This article belongs to the Special Issue Numerical Analysis, Approximation Theory and Related Topics)
28 pages, 621 KB  
Article
Averaging Principle for Itô–Doob Fractional Stochastic Systems in mth Moment
by Muhammad Imran Liaqat and Ramy M. Hafez
Axioms 2026, 15(4), 262; https://doi.org/10.3390/axioms15040262 - 4 Apr 2026
Viewed by 308
Abstract
This study presents results on the well-posedness, Ulam–Hyers stability, and mth moment averaging principle for the Itô–Doob fractional stochastic system within the framework of η-Caputo fractional derivatives. We demonstrate well-posedness using the fixed-point approach. A generalized Grönwall inequality is employed to [...] Read more.
This study presents results on the well-posedness, Ulam–Hyers stability, and mth moment averaging principle for the Itô–Doob fractional stochastic system within the framework of η-Caputo fractional derivatives. We demonstrate well-posedness using the fixed-point approach. A generalized Grönwall inequality is employed to establish sufficient conditions for Ulam–Hyers stability. Furthermore, we establish the averaging principle that facilitates obtaining a simplified averaged system from the original complex, multiple time-scale system. Finally, numerical simulations using the Euler–Maruyama method are provided to support the theoretical findings. Full article
(This article belongs to the Special Issue Numerical Analysis, Approximation Theory and Related Topics)
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12 pages, 318 KB  
Article
Sharp Unified Smoothness Theory for Cavalieri Estimation via Fourier Decay
by Francisco-Javier Soto
Axioms 2025, 14(11), 786; https://doi.org/10.3390/axioms14110786 - 26 Oct 2025
Cited by 1 | Viewed by 721
Abstract
Cavalieri estimation is a widely used technique in stereology (applied geometric sampling) for approximating the volume of a solid by sampling cross-sectional areas along a fixed axis. Classical theory shows that, under systematic equidistant sampling (the well-known Cavalieri estimator), the variance decay depends [...] Read more.
Cavalieri estimation is a widely used technique in stereology (applied geometric sampling) for approximating the volume of a solid by sampling cross-sectional areas along a fixed axis. Classical theory shows that, under systematic equidistant sampling (the well-known Cavalieri estimator), the variance decay depends on the smoothness of the area function, which is essentially measured by the number of continuous derivatives. This paper focuses on the natural assumptions under which the theory holds. We first obtain sharp and explicit variance rates: when the Fourier decay is of order s>1/2, the variance of the Cavalieri estimator decays as t2s with a constant independent of t. Building on this, we show that the smoothness condition expressed in terms of the algebraic Fourier decay subsumes both integer- and fractional-order frameworks used to date. Finally, we establish a matching converse showing that, under general assumptions, no broader smoothness framework extends the theory; that is, any algebraic variance decay implies the corresponding Fourier decay. Full article
(This article belongs to the Special Issue Numerical Analysis, Approximation Theory and Related Topics)
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