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Symmetry
Special Issues
Ordinary and Partial Differential Equations: Theory and Application
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Ordinary and Partial Differential Equations: Theory and Application

A special issue of Symmetry (ISSN 2073-8994).

Deadline for manuscript submissions: closed (31 December 2019) | Viewed by 7365

Special Issue Editor

Prof. Dr. Clemente Cesarano

E-Mail Website
Guest Editor
Section of Mathematics, International Telematic University, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy
Interests: special functions; orthogonal polynomials; differential equations; operator theory; multivariate approximation theory; Lie algebra
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The study of differential equations is useful for understanding natural phenomena. In this Special Issue, we aim to present the latest research on the properties of ODE (Ordinary Differential Equations) and PDE (Partial Differential Equations) related to different techniques for finding solutions and methods describing the nature of these solutions or their related approximations.

In addition, we welcome papers on numerical aspects using classical or non-standard approaches, for example, the concepts and related formalism of special functions. Furthermore, articles on fractional differential equations are of interest, as are contributions related to the symmetry approach to problems of integrability in the field of differential equations.

Prof. Clemente Cesarano
Guest Editor

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. Symmetry 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

  • symmetries
  • Ordinary Differential Equations
  • Partial Differential Equations
  • numerical methods
  • fractional calculus

Published Papers (3 papers)

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Research

9 pages, 272 KiB  
Article
Particular Solutions of Ordinary Differential Equations Using Discrete Symmetry Groups
by Khudija Bibi
Symmetry 2020, 12(1), 180; https://doi.org/10.3390/sym12010180 - 19 Jan 2020
Cited by 8 | Viewed by 2889
Abstract
This article explains how discrete symmetry groups can be directly applied to obtain the particular solutions of nonlinear ordinary differential equations (ODEs). The particular solutions of some nonlinear ordinary differential equations have been generated by means of their discrete symmetry groups. Full article
(This article belongs to the Special Issue Ordinary and Partial Differential Equations: Theory and Application)
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11 pages, 294 KiB  
Article
A Class of Critical Magnetic Fractional Kirchhoff Problems
by Jiabin Zuo, Tianqing An and Guoju Ye
Symmetry 2020, 12(1), 76; https://doi.org/10.3390/sym12010076 - 02 Jan 2020
Cited by 4 | Viewed by 1621
Abstract
In this paper, we deal with the existence and asymptotic behavior of solutions for a fractional Kirchhoff type problem involving the electromagnetic fields and critical nonlinearity by using the classical critical point theorem. Meanwhile, an example is given to illustrate the application of [...] Read more.
In this paper, we deal with the existence and asymptotic behavior of solutions for a fractional Kirchhoff type problem involving the electromagnetic fields and critical nonlinearity by using the classical critical point theorem. Meanwhile, an example is given to illustrate the application of the main result. Full article
(This article belongs to the Special Issue Ordinary and Partial Differential Equations: Theory and Application)
12 pages, 247 KiB  
Article
Analytical Solution of Linear Fractional Systems with Variable Coefficients Involving Riemann–Liouville and Caputo Derivatives
by Ivan Matychyn
Symmetry 2019, 11(11), 1366; https://doi.org/10.3390/sym11111366 - 04 Nov 2019
Cited by 14 | Viewed by 2119
Abstract
This paper deals with the initial value problem for linear systems of fractional differential equations (FDEs) with variable coefficients involving Riemann–Liouville and Caputo derivatives. Some basic properties of fractional derivatives and antiderivatives, including their non-symmetry w.r.t. each other, are discussed. The technique of [...] Read more.
This paper deals with the initial value problem for linear systems of fractional differential equations (FDEs) with variable coefficients involving Riemann–Liouville and Caputo derivatives. Some basic properties of fractional derivatives and antiderivatives, including their non-symmetry w.r.t. each other, are discussed. The technique of the generalized Peano–Baker series is used to obtain the state-transition matrix. Explicit solutions are derived both in the homogeneous and inhomogeneous case. The theoretical results are supported by examples. Full article
(This article belongs to the Special Issue Ordinary and Partial Differential Equations: Theory and Application)
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