Nonlinear Problems in Mathematical Physics

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

Deadline for manuscript submissions: closed (31 January 2023) | Viewed by 1810

Special Issue Editor


E-Mail Website
Guest Editor
Department of Applied Mathematics and Didactics, Universidad a Distancia de Madrid (UDIMA), 28400 Madrid, Spain
Interests: diffusion modeling; p-Laplacian operators; phase change materials; Darcy-Forchheimer fluids; porous media flow modelling; rheological properties; magnetohydrodynamics; geometric perturbation theory; travelling waves; solitons; peakons; flame modeling
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The modeling of nonlinear problems is key in applied sciences. Solutions to these problems are typically searched for using different methodologies, from qualitative approaches to quantitative theories. 

This Special Issue hopes to draw a linkage between the different methodologies and real-world applications. Articles providing a comprehensive view of nonlinear problems together with techniques for their solution are welcome. We welcome analyses focused on purely analytical or numerical techniques, but it is recommended to provide hybrid analysis from both sides. Papers dealing with the following topics are welcome:

  • Operators theory in PDE (p-Laplacian, poly-Laplacian, porous medium equation, high order, doubly nonlinear diffusion, etc.).
  • Analysis of solutions in differential and difference equations.
  • Mathematical problems in multiphysics.
  • Mathematical modelling theory.
  • Optimization theory and applications.
  • Approximation theory and applications.
  • Symmetries in mathematical physics.
  • Differential geometry theory and applications.
  • Harmonic analysis and applications.
  • Low-regularity spaces theory and applications.

Dr. José Luis Díaz
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. 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.

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.

Further information on MDPI's Special Issue polices can be found here.

Published Papers (1 paper)

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

Research

15 pages, 526 KiB  
Article
Solving a Generalized Fractional Nonlinear Integro-Differential Equations via Modified Sumudu Decomposition Transform
by Kamel Al-Khaled
Axioms 2022, 11(8), 398; https://doi.org/10.3390/axioms11080398 - 11 Aug 2022
Cited by 2 | Viewed by 1422
Abstract
The Sumudu decomposition method was used and developed in this paper to find approximate solutions for a general form of fractional integro-differential equation of Volterra and Fredholm types. The Caputo definition was used to deal with fractional derivatives. As the method under consideration [...] Read more.
The Sumudu decomposition method was used and developed in this paper to find approximate solutions for a general form of fractional integro-differential equation of Volterra and Fredholm types. The Caputo definition was used to deal with fractional derivatives. As the method under consideration depends mainly on writing non-linear terms, which are often found inside the kernel of the integral equation, writing it in the form of Adomian’s polynomials in the well-known way. After applying the Sumudu transformation to both sides of the integral equation, the solution was written in the form of a convergent infinite series whose terms can be alternately calculated. The method was applied to three examples of non-linear integral equations with fractional derivatives. The results that were presented in the form of tables and graphs showed that the method is accurate, effective and highly efficient. Full article
(This article belongs to the Special Issue Nonlinear Problems in Mathematical Physics)
Show Figures

Figure 1

Back to TopTop