Special Issue "Recent Advances in Differential Equations and Applications"

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

Deadline for manuscript submissions: 31 August 2021.

Special Issue Editors

Prof. Dr. Juan Carlos Cortés López
E-Mail Website
Guest Editor
Department of Applied Mathematics and Institute for Multidisciplinary Mathematics (im2), Universitat Politècnica de València, 46022 Valencia, Spain
Interests: differential equations with randomness; mathematical modelling
Special Issues and Collections in MDPI journals

Special Issue Information

Dear Colleagues,

Differential equations play a key role in modelling the dynamics of many phenomena belonging to different realms including physics, chemistry, finance, and social sciences. Since their classical formulation, via ordinary derivatives, a number of other classes of differential equations have been proposed, such as delay, fractional, functional, or integro-differential equations. The mathematical and numerical analyses of all these types of differential equations are still a hot topic in mathematics. This interest increased when the aforementioned types of differential equations consider the randomness often present in mathematical modelling, which lead to random and stochastic differential equations.

In this Special Issue, we encourage submissions providing new results in the setting of differential equations and their applications. Potential topics include, but are not limited to the next keywords (see below).

Prof. Juan Ramón Torregrosa Sánchez
Prof. Alicia Cordero Barbero
Prof. Juan Carlos Cortés López
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 papers will be 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 1600 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

  • Ordinary and partial differential equations
  • Differential-difference equations
  • Delay differential equations
  • Fractional differential equations
  • Algebraic-differential equations
  • Integro-differential equations
  • Complex differential equations
  • Functional differential equations
  • Numerical methods for differential equations
  • Stability theory
  • Random and stochastic differential equations
  • Mathematical modelling using differential equations

Published Papers (5 papers)

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Research

Article
Oscillation of Second-Order Differential Equations with Multiple and Mixed Delays under a Canonical Operator
Mathematics 2021, 9(12), 1323; https://doi.org/10.3390/math9121323 - 08 Jun 2021
Viewed by 221
Abstract
In this work, we obtained new sufficient and necessary conditions for the oscillation of second-order differential equations with mixed and multiple delays under a canonical operator. Our methods could be applicable to find the sufficient and necessary conditions for any neutral differential equations. [...] Read more.
In this work, we obtained new sufficient and necessary conditions for the oscillation of second-order differential equations with mixed and multiple delays under a canonical operator. Our methods could be applicable to find the sufficient and necessary conditions for any neutral differential equations. Furthermore, we proved the validity of the obtained results via particular examples. At the end of the paper, we provide the future scope of this study. Full article
(This article belongs to the Special Issue Recent Advances in Differential Equations and Applications)
Article
Generalization of Quantum Ostrowski-Type Integral Inequalities
Mathematics 2021, 9(10), 1155; https://doi.org/10.3390/math9101155 - 20 May 2021
Viewed by 290
Abstract
In this paper, we prove some new Ostrowski-type integral inequalities for q-differentiable bounded functions. It is also shown that the results presented in this paper are a generalization of know results in the literarure. Applications to special means are also discussed. Full article
(This article belongs to the Special Issue Recent Advances in Differential Equations and Applications)
Article
On the Numerical Simulation of HPDEs Using θ-Weighted Scheme and the Galerkin Method
Mathematics 2021, 9(1), 78; https://doi.org/10.3390/math9010078 - 31 Dec 2020
Viewed by 466
Abstract
Herein, an efficient algorithm is proposed to solve a one-dimensional hyperbolic partial differential equation. To reach an approximate solution, we employ the θ-weighted scheme to discretize the time interval into a finite number of time steps. In each step, we have a linear ordinary differential equation. Applying the Galerkin method based on interpolating scaling functions, we can solve this ODE. Therefore, in each time step, the solution can be found as a continuous function. Stability, consistency, and convergence of the proposed method are investigated. Several numerical examples are devoted to show the accuracy and efficiency of the method and guarantee the validity of the stability, consistency, and convergence analysis. Full article
(This article belongs to the Special Issue Recent Advances in Differential Equations and Applications)
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Article
Nonlinear Observability Algorithms with Known and Unknown Inputs: Analysis and Implementation
Mathematics 2020, 8(11), 1876; https://doi.org/10.3390/math8111876 - 29 Oct 2020
Viewed by 622
Abstract
The observability of a dynamical system is affected by the presence of external inputs, either known (such as control actions) or unknown (disturbances). Inputs of unknown magnitude are especially detrimental for observability, and they also complicate its analysis. Hence, the availability of computational [...] Read more.
The observability of a dynamical system is affected by the presence of external inputs, either known (such as control actions) or unknown (disturbances). Inputs of unknown magnitude are especially detrimental for observability, and they also complicate its analysis. Hence, the availability of computational tools capable of analysing the observability of nonlinear systems with unknown inputs has been limited until lately. Two symbolic algorithms based on differential geometry, ORC-DF and FISPO, have been recently proposed for this task, but their critical analysis and comparison is still lacking. Here we perform an analytical comparison of both algorithms and evaluate their performance on a set of problems, while discussing their strengths and limitations. Additionally, we use these analyses to provide insights about certain aspects of the relationship between inputs and observability. We found that, while ORC-DF and FISPO follow a similar approach, they differ in key aspects that can have a substantial influence on their applicability and computational cost. The FISPO algorithm is more generally applicable, since it can analyse any nonlinear ODE model. The ORC-DF algorithm analyses models that are affine in the inputs, and if those models have known inputs it is sometimes more efficient. Thus, the optimal choice of a method depends on the characteristics of the problem under consideration. To facilitate the use of both algorithms, we implemented the ORC-DF condition in a new version of STRIKE-GOLDD, a MATLAB toolbox for structural identifiability and observability analysis. Since this software tool already had an implementation of the FISPO algorithm, the new release allows modellers and model users the convenience of choosing between different algorithms in a single tool, without changing the coding of their model. Full article
(This article belongs to the Special Issue Recent Advances in Differential Equations and Applications)
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Article
Group Invariant Solutions and Conserved Quantities of a (3+1)-Dimensional Generalized Kadomtsev–Petviashvili Equation
Mathematics 2020, 8(6), 1012; https://doi.org/10.3390/math8061012 - 20 Jun 2020
Cited by 1 | Viewed by 476
Abstract
In this work, we investigate a (3+1)-dimensional generalised Kadomtsev–Petviashvili equation, recently introduced in the literature. We determine its group invariant solutions by employing Lie symmetry methods and obtain elliptic, rational and logarithmic solutions. The solutions derived in this paper are the most general [...] Read more.
In this work, we investigate a (3+1)-dimensional generalised Kadomtsev–Petviashvili equation, recently introduced in the literature. We determine its group invariant solutions by employing Lie symmetry methods and obtain elliptic, rational and logarithmic solutions. The solutions derived in this paper are the most general since they contain elliptic functions. Finally, we derive the conserved quantities of this equation by employing two approaches—the general multiplier approach and Ibragimov’s theorem. The importance of conservation laws is explained in the introduction. It should be pointed out that the investigation of higher dimensional nonlinear partial differential equations is vital to our perception of the real world since they are more realistic models of natural and man-made phenomena. Full article
(This article belongs to the Special Issue Recent Advances in Differential Equations and Applications)
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