Special Issue "Nonlinear Equations: Theory, Methods, and Applications II"

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

Deadline for manuscript submissions: 30 April 2022.

Special Issue Editors

Prof. Dr. Ravi P. Agarwal
grade E-Mail Website
Guest Editor
Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363, USA
Interests: nonlinear analysis; differential and difference equations; fixed point theory; general inequalities
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Bashir Ahmad
E-Mail Website
Guest Editor
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia
Interests: differential equations; boundary value problems; nonlinear analysis; applications
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

It is our pleasure to announce the launch of a new Special Issue of Mathematics on the topic of “Nonlinear Equations: Theory, Methods, and Applications II”. While the list below is by no means exclusive, some of the topics we would be interested in covering in this Special Issue include:

  • Ordinary differential equations;
  • Delay differential equations;
  • Functional equations;
  • Equations on time scales;
  • Partial differential equations;
  • Fractional differential equations;
  • Stochastic differential equations;
  • Integral equations;
  • Applications of Fixed-Point Theorems to Nonlinear Equations.

We look forward to your contributions.

Prof. Dr. Ravi P. Agarwal
Prof. Dr. Bashir Ahmad
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.

Published Papers (5 papers)

Order results
Result details
Select all
Export citation of selected articles as:

Research

Article
Existence of Positive Solutions for a Higher-Order Fractional Differential Equation with Multi-Term Lower-Order Derivatives
Mathematics 2021, 9(23), 3031; https://doi.org/10.3390/math9233031 - 26 Nov 2021
Viewed by 94
Abstract
This paper deals with the study of the existence of positive solutions for a class of nonlinear higher-order fractional differential equations in which the nonlinear term contains multi-term lower-order derivatives. By reducing the order of the highest derivative, the higher-order fractional differential equation [...] Read more.
This paper deals with the study of the existence of positive solutions for a class of nonlinear higher-order fractional differential equations in which the nonlinear term contains multi-term lower-order derivatives. By reducing the order of the highest derivative, the higher-order fractional differential equation is transformed into a lower-order fractional differential equation. Then, combining with the properties of left-sided Riemann–Liouville integral operators, we obtain the existence of the positive solutions of fractional differential equations utilizing some weaker conditions. Furthermore, some examples are given to demonstrate the validity of our main results. Full article
(This article belongs to the Special Issue Nonlinear Equations: Theory, Methods, and Applications II)
Show Figures

Figure 1

Article
Some Inequalities of Extended Hypergeometric Functions
Mathematics 2021, 9(21), 2702; https://doi.org/10.3390/math9212702 - 25 Oct 2021
Viewed by 397
Abstract
Hypergeometric functions and their inequalities have found frequent applications in various fields of mathematical sciences. Motivated by the above, we set up certain inequalities including extended type Gauss hypergeometric function and confluent hypergeometric function, respectively, by virtue of Hölder integral inequality and Chebyshev’s [...] Read more.
Hypergeometric functions and their inequalities have found frequent applications in various fields of mathematical sciences. Motivated by the above, we set up certain inequalities including extended type Gauss hypergeometric function and confluent hypergeometric function, respectively, by virtue of Hölder integral inequality and Chebyshev’s integral inequality. We also studied the monotonicity, log-concavity, and log-convexity of extended hypergeometric functions, which are derived by using the inequalities on an extended beta function. Full article
(This article belongs to the Special Issue Nonlinear Equations: Theory, Methods, and Applications II)
Article
An Investigation of an Integral Equation Involving Convex–Concave Nonlinearities
Mathematics 2021, 9(19), 2372; https://doi.org/10.3390/math9192372 - 24 Sep 2021
Viewed by 268
Abstract
We investigate the existence and uniqueness of positive solutions to an integral equation involving convex or concave nonlinearities. A numerical algorithm based on Picard iterations is provided to obtain an approximation of the unique solution. The main tools used in this work are [...] Read more.
We investigate the existence and uniqueness of positive solutions to an integral equation involving convex or concave nonlinearities. A numerical algorithm based on Picard iterations is provided to obtain an approximation of the unique solution. The main tools used in this work are based on partial-ordering methods and fixed-point theory. Our results are supported by examples. Full article
(This article belongs to the Special Issue Nonlinear Equations: Theory, Methods, and Applications II)
Article
Analysis of the Time Fractional-Order Coupled Burgers Equations with Non-Singular Kernel Operators
Mathematics 2021, 9(18), 2326; https://doi.org/10.3390/math9182326 - 19 Sep 2021
Viewed by 371
Abstract
In this article, we have investigated the fractional-order Burgers equation via Natural decomposition method with nonsingular kernel derivatives. The two types of fractional derivatives are used in the article of Caputo–Fabrizio and Atangana–Baleanu derivative. We employed Natural transform on fractional-order Burgers equation followed [...] Read more.
In this article, we have investigated the fractional-order Burgers equation via Natural decomposition method with nonsingular kernel derivatives. The two types of fractional derivatives are used in the article of Caputo–Fabrizio and Atangana–Baleanu derivative. We employed Natural transform on fractional-order Burgers equation followed by inverse Natural transform, to achieve the result of the equations. To validate the method, we have considered a two examples and compared with the exact results. Full article
(This article belongs to the Special Issue Nonlinear Equations: Theory, Methods, and Applications II)
Show Figures

Figure 1

Article
Investigation of the Fractional Strongly Singular Thermostat Model via Fixed Point Techniques
Mathematics 2021, 9(18), 2298; https://doi.org/10.3390/math9182298 - 17 Sep 2021
Viewed by 362
Abstract
Our main purpose in this paper is to prove the existence of solutions for the fractional strongly singular thermostat model under some generalized boundary conditions. In this way, we use some recent nonlinear fixed-point techniques involving α-ψ-contractions and α-admissible [...] Read more.
Our main purpose in this paper is to prove the existence of solutions for the fractional strongly singular thermostat model under some generalized boundary conditions. In this way, we use some recent nonlinear fixed-point techniques involving α-ψ-contractions and α-admissible maps. Further, we establish the similar results for the hybrid version of the given fractional strongly singular thermostat control model. Some examples are studied to illustrate the consistency of our results. Full article
(This article belongs to the Special Issue Nonlinear Equations: Theory, Methods, and Applications II)
Back to TopTop