Special Issue "New Challenges Arising in Engineering Problems with Fractional and Integer Order"

A special issue of Fractal and Fractional (ISSN 2504-3110).

Deadline for manuscript submissions: 1 December 2020.

Special Issue Editors

Prof. Dr. Haci Mehmet Baskonus
Website SciProfiles
Guest Editor
Department of Mathematics and Science Education, Faculty of Education, Harran University, Sanliurfa 63100, Turkey
Interests: partial differential equations; fractional calculus; analytical methods; numerical methods; mathematical physics
Prof. Dr. Luis Manuel Sánchez Ruiz

Guest Editor
ETSID-Departamento de Matemática Aplicada & CITG, Universitat Politecnica de Valencia, E-46022 Valencia, Spain
Interests: applied mathematics; engineering education; functional analysis with theoretical and applied
Prof. Dr. Armando Ciancio

Guest Editor
Department of Biomedical and Dental Sciences and Morphofunctional Imaging, University of Messina, 98125 Messina, Italy
Interests: time series based on wavelets; analysis of solutions in the field of physical-mathematical models of rheological media; fractional calculus; mathematical models in economics and finance; physical-mathematical models for biological media and applications to biotechnological and medical sciences

Special Issue Information

Dear Colleagues,

Recently, many new models have been developed that deal with real-world problems that are seen as serious threats to the future of human kind. This comes from modeling events observed in various fields of science, such as physics, chemistry, mechanics, electricity, biology, economy, mathematical applications, and control theory. Moreover, research done on fractional ordinary or partial differential equations and other relevant topics relating to integer order have attracted the attention of experts from all over the world.

The focus of this Special Issue will be on reviewing new developments based on fractional differentiation and integration, both with respect to theoretical and numerical aspects.

This Special Issue is a place for experts to share new ideas on theories, applications, numerical and analytical methods and simulations of fractional calculus and fractional differential equations, as well as integer order. Topics of interest are defined below, and submissions relating to relevant fields are welcome.

  • New analytical and numerical methods to solve partial differential equations
  • Computational methods for fractional differential equations
  • Analysis, modeling, and control of phenomena in the following:
    • Electrical engineering;
    • Fluids dynamics and thermal engineering;
    • Mechanics;
    • Biology;
    • Physics;
    • Applied sciences;
    • Computer science.
  • Engineering problems
  • Deterministic and stochastic fractional order models

This Special Issue is organized together with the 5th International Conference on Computational Mathematics and Engineering Sciences (CMES-2020) (1–3 July 2020, Van, Turkey); hence, participants in CMES-2020 are especially welcome to submit their contributions. However, this Special Issue will accept contributions from all authors, not just conference participants.

Prof. Dr. Haci Mehmet Baskonus
Prof. Dr. Luis Manuel Sánchez Ruiz
Prof. Dr. Armando Ciancio
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. Fractal and Fractional is an international peer-reviewed open access quarterly 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 1000 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)

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Research

Open AccessArticle
Laplace Transform Method for Economic Models with Constant Proportional Caputo Derivative
Fractal Fract 2020, 4(3), 30; https://doi.org/10.3390/fractalfract4030030 - 03 Jul 2020
Abstract
In this study, we solved the economic models based on market equilibrium with constant proportional Caputo derivative using the Laplace transform. We proved the accuracy and efficiency of the method. We constructed the relations between the solutions of the problems and bivariate Mittag–Leffler [...] Read more.
In this study, we solved the economic models based on market equilibrium with constant proportional Caputo derivative using the Laplace transform. We proved the accuracy and efficiency of the method. We constructed the relations between the solutions of the problems and bivariate Mittag–Leffler functions. Full article
Open AccessArticle
Numerical Solution of Fractional Order Burgers’ Equation with Dirichlet and Neumann Boundary Conditions by Reproducing Kernel Method
Fractal Fract 2020, 4(2), 27; https://doi.org/10.3390/fractalfract4020027 - 19 Jun 2020
Abstract
In this research, obtaining of approximate solution for fractional-order Burgers’ equation will be presented in reproducing kernel Hilbert space (RKHS). Some special reproducing kernel spaces are identified according to inner products and norms. Then an iterative approach is constructed by using kernel functions. [...] Read more.
In this research, obtaining of approximate solution for fractional-order Burgers’ equation will be presented in reproducing kernel Hilbert space (RKHS). Some special reproducing kernel spaces are identified according to inner products and norms. Then an iterative approach is constructed by using kernel functions. The convergence of this approach and its error estimates are given. The numerical algorithm of the method is presented. Furthermore, numerical outcomes are shown with tables and graphics for some examples. These outcomes demonstrate that the proposed method is convenient and effective. Full article
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Open AccessArticle
On the Fractional Maximal Delta Integral Type Inequalities on Time Scales
Fractal Fract 2020, 4(2), 26; https://doi.org/10.3390/fractalfract4020026 - 17 Jun 2020
Abstract
Time scales have been the target of work of many mathematicians for more than a quarter century. Some of these studies are of inequalities and dynamic integrals. Inequalities and fractional maximal integrals have an important place in these studies. For example, inequalities and [...] Read more.
Time scales have been the target of work of many mathematicians for more than a quarter century. Some of these studies are of inequalities and dynamic integrals. Inequalities and fractional maximal integrals have an important place in these studies. For example, inequalities and integrals contributed to the solution of many problems in various branches of science. In this paper, we will use fractional maximal integrals to establish integral inequalities on time scales. Moreover, our findings show that inequality is valid for discrete and continuous conditions. Full article
Open AccessArticle
Exact Solution of Two-Dimensional Fractional Partial Differential Equations
Fractal Fract 2020, 4(2), 21; https://doi.org/10.3390/fractalfract4020021 - 12 May 2020
Abstract
In this study, we examine adapting and using the Sumudu decomposition method (SDM) as a way to find approximate solutions to two-dimensional fractional partial differential equations and propose a numerical algorithm for solving fractional Riccati equation. This method is a combination of the [...] Read more.
In this study, we examine adapting and using the Sumudu decomposition method (SDM) as a way to find approximate solutions to two-dimensional fractional partial differential equations and propose a numerical algorithm for solving fractional Riccati equation. This method is a combination of the Sumudu transform method and decomposition method. The fractional derivative is described in the Caputo sense. The results obtained show that the approach is easy to implement and accurate when applied to various fractional differential equations. Full article
Open AccessArticle
Fractional Kinetic Equations Associated with Incomplete I-Functions
Fractal Fract 2020, 4(2), 19; https://doi.org/10.3390/fractalfract4020019 - 04 May 2020
Abstract
In this paper, we investigate the solution of fractional kinetic equation (FKE) associated with the incomplete I-function (IIF) by using the well-known integral transform (Laplace transform). The FKE plays a great role in solving astrophysical problems. The solutions are represented in terms [...] Read more.
In this paper, we investigate the solution of fractional kinetic equation (FKE) associated with the incomplete I-function (IIF) by using the well-known integral transform (Laplace transform). The FKE plays a great role in solving astrophysical problems. The solutions are represented in terms of IIF. Next, we present some interesting corollaries by specializing the parameters of IIF in the form of simpler special functions and also mention a few known results, which are very useful in solving physical or real-life problems. Finally, some graphical results are presented to demonstrate the influence of the order of the fractional integral operator on the reaction rate. Full article
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