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Advances in Integral Equations and Transforms: Theory and Applications in...
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Advances in Integral Equations and Transforms: Theory and Applications in Science and Engineering

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Difference and Differential Equations".

Deadline for manuscript submissions: closed (30 September 2023) | Viewed by 2911

Special Issue Editors

Dr. Maria Dobriţoiu

E-Mail Website
Guest Editor
Department of Mathematics and Computer Science, University of Petroşani, 332006 Petrosani, Romania
Interests: integral equations; differential equations; fixed point theory
Prof. Dr. Wilhelm W. Kecs

E-Mail Website
Guest Editor
Department of Mathematics and Computer Science, University of Petroşani, 332047 Petrosani, Romania
Interests: distribution theory; mechanics of deformable solids

Special Issue Information

Dear Colleagues,

As you know, there has always been a special interest in modeling dynamic processes in various diverse areas of mathematical and engineering sciences. Many families of integral equations and transforms have been used and developed from both the theoretical and applied perspectives. Intensive work into real-world and other interdisciplinary applications covers a lot of novel theoretical analysis into the existence, uniqueness, and stability of the solutions of these equations and transforms. Moreover, there is genuine need for new analytical and numerical methods and techniques for solving these equations.

Interested authors are cordially invited to present original research articles as well as review articles in the area of integral equations and transforms. This Special Issue will be an international forum for researchers to present the most recent developments and ideas in the field. The topics of interest for this Special Issue include, but are not limited to, results regarding: 

  • Mathematical models governed by integral equations;
  • The existence, uniqueness, and stability of the solutions;
  • Data dependence, and the differentiability of the solutions;
  • Solution comparison theorems;
  • Gronwall lemmas and integral inequalities;
  • The approximation of the solution, including related numerical methods;
  • Numerical methods for the approximate calculation of the integrals;
  • The use of specific software to calculate approximate solutions of integral equations;
  • Integral transforms, their related operational calculus, and related transforms topics;
  • The applications of the use of integral equations in various fields, including engineering, physics, mechanics, chemistry, biology, medicine, economics, etc.

Papers on the real-world and other interdisciplinary applications are, also, especially welcome.

In addition, you may include some of the many other aspects that may be part of this vast field, connected as they are by differential equations and, especially, by partial differential equations, all of which lead to computational and applied mathematics.

Dr. Maria Dobriţoiu
Prof. Dr. Wilhelm W. Kecs
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. 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

  • differential, partial differential, and integral equations
  • functional integral equations
  • linear and nonlinear problems
  • systems of integral equations
  • existence and uniqueness of solutions
  • properties of the solution: data dependence, differentiability, solutions comparison, and stability
  • integral inequalities
  • integral transforms
  • numerical methods for integral equations
  • convergence analysis
  • mathematical models using integral equations
  • applications of the use of integral equations in various fields

Published Papers (3 papers)

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Research

13 pages, 305 KiB  
Article
On Erdélyi–Kober Fractional Operator and Quadratic Integral Equations in Orlicz Spaces
by Mohamed M. A. Metwali and Shami A. M. Alsallami
Mathematics 2023, 11(18), 3901; https://doi.org/10.3390/math11183901 - 13 Sep 2023
Cited by 1 | Viewed by 739
Abstract
We provide and prove some new fundamental properties of the Erdélyi–Kober (EK) fractional operator, including monotonicity, boundedness, acting, and continuity in both Lebesgue spaces (Lp) and Orlicz spaces (Lφ). We employ these properties with the [...] Read more.
We provide and prove some new fundamental properties of the Erdélyi–Kober (EK) fractional operator, including monotonicity, boundedness, acting, and continuity in both Lebesgue spaces (Lp) and Orlicz spaces (Lφ). We employ these properties with the concept of the measure of noncompactness (MNC) associated with the fixed-point hypothesis (FPT) in solving a quadratic integral equation of fractional order in Lp,p≥1 and Lφ. Finally, we provide a few examples to support our findings. Our suppositions can be successfully applied to various fractional problems. Full article
(This article belongs to the Special Issue Advances in Integral Equations and Transforms: Theory and Applications in Science and Engineering)
25 pages, 450 KiB  
Article
Applications of the Tarig Transform and Hyers–Ulam Stability to Linear Differential Equations
by L. Chitra, K. Alagesan, Vediyappan Govindan, Salman Saleem, A. Al-Zubaidi and C. Vimala
Mathematics 2023, 11(12), 2778; https://doi.org/10.3390/math11122778 - 20 Jun 2023
Cited by 1 | Viewed by 767
Abstract
In this manuscript, we discuss the Tarig transform for homogeneous and non-homogeneous linear differential equations. Using this Tarig integral transform, we resolve higher-order linear differential equations, and we produce the conditions required for Hyers–Ulam stability. This is the first attempt to use the [...] Read more.
In this manuscript, we discuss the Tarig transform for homogeneous and non-homogeneous linear differential equations. Using this Tarig integral transform, we resolve higher-order linear differential equations, and we produce the conditions required for Hyers–Ulam stability. This is the first attempt to use the Tarig transform to show that linear and nonlinear differential equations are stable. This study also demonstrates that the Tarig transform method is more effective for analyzing the stability issue for differential equations with constant coefficients. A discussion of applications follows, to illustrate our approach. This research also presents a novel approach to studying the stability of differential equations. Furthermore, this study demonstrates that Tarig transform analysis is more practical for examining stability issues in linear differential equations with constant coefficients. In addition, we examine some applications of linear, nonlinear, and fractional differential equations, by using the Tarig integral transform. Full article
(This article belongs to the Special Issue Advances in Integral Equations and Transforms: Theory and Applications in Science and Engineering)
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13 pages, 319 KiB  
Article
Feynman Integrals for the Harmonic Oscillator in an Exponentially Growing Potential
by Alviu Rey Nasir, Jingle Magallanes, Jinky Bornales and José Luís Da Silva
Mathematics 2023, 11(7), 1632; https://doi.org/10.3390/math11071632 - 28 Mar 2023
Viewed by 845
Abstract
We construct the Feynman integral for the Schrödinger propagator with combinations of exponentially growing and harmonic oscillator potentials as well-defined white noise functionals. Full article
(This article belongs to the Special Issue Advances in Integral Equations and Transforms: Theory and Applications in Science and Engineering)
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