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Fractal Fract
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Recent Advances in Computational Physics with Fractional Application, 2nd Edition
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Recent Advances in Computational Physics with Fractional Application, 2nd Edition

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: 31 December 2024 | Viewed by 8360

Special Issue Editors

Dr. Lanre Akinyemi

E-Mail Website
Guest Editor
Department of Mathematics, Hampton University, Hampton, VA 23669, USA
Interests: fractional differential equations and their applications; methods and applications of nonlinear equations; iteration methods for differential equations; numerical and analytical methods for differential equations; mathematical modeling of flow in porous media
Special Issues, Collections and Topics in MDPI journals
Dr. Mehmet Senol

E-Mail Website
Guest Editor
Department of Mathematics, Nevşehir Haci Bektaş Veli Üniversitesi, Nevsehir 50300, Turkey
Interests: numerical and analytical methods for differential equations; numerical analysis; fractional differential equations and their applications
Special Issues, Collections and Topics in MDPI journals
Dr. Solomon Manukure

E-Mail Website
Guest Editor
Department of Mathematics, Florida A & M University, Tallahassee, FL 32307, USA
Interests: partial differential equations; nonlinear wave theory; integrable systems; soliton theory; Hamiltonian systems; algebro-geometric solutions; Riemann–Hilbert problem
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue is devoted to “Recent Advances in Computational Physics with Fractional Application”.

Fractional calculus, a generalization of integer-order differentiation and integration, has applications in diverse and widespread fields of applied sciences and engineering, such as in image processing, financial modeling, control theory for dynamical systems, disease modeling, nanotechnology, random walks, anomalous transport and anomalous diffusion, viscoelasticity, as well as many others.

Nonlinear partial differential equations are used to explain a wide range of physical phenomena that arise in applied physics, including fluid dynamics, plasma physics, solid mechanics, and quantum field theory. Many of these equations are nonlinear and are thus frequently difficult to solve explicitly. Some direct and systematic methods have been developed to study nonlinear partial differential equations, such as the extended Tanh-function method, sub-equation method, inverse scattering method, G′/G expansion method, simplest method, Painlevé analysis, Cole–Hopf transformation, inverse scattering method, the Bäcklund transformation method, Hirota bilinear method, sine-Gordon expansion method, generalized auxiliary equation method, Kudryashov method, and many more.

As a result of recent developments in fractional calculus applications, many researchers have become interested in this field. This Special Issue on “Recent Advances in Computational Physics with Fractional Application” is devoted to uncovering leading researchers’ recent work in the above fields of fractional calculus.

Dr. Lanre Akinyemi
Dr. Mehmet Senol
Dr. Solomon Manukure
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 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. Fractal and Fractional 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 2700 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

  • stability analysis
  • integral equations
  • semi-analytical method
  • mathematical modeling
  • traveling wave solutions
  • analytical and numerical methods
  • soliton theory and its applications
  • fractional calculus and its applications
  • ordinary and partial differential equations
  • symmetry analysis and conservation laws
  • mathematical modeling of flow in porous media
  • high-order numerical differential formulas for fractional derivatives
  • numerical and computational methods in fractional differential equations

Related Special Issue

Published Papers (7 papers)

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Research

16 pages, 3262 KiB  
Article
Extracting the Ultimate New Soliton Solutions of Some Nonlinear Time Fractional PDEs via the Conformable Fractional Derivative
by Md Ashik Iqbal, Abdul Hamid Ganie, Md Mamun Miah and Mohamed S. Osman
Fractal Fract. 2024, 8(4), 210; https://doi.org/10.3390/fractalfract8040210 - 03 Apr 2024
Viewed by 1202
Abstract
Nonlinear fractional-order differential equations have an important role in various branches of applied science and fractional engineering. This research paper shows the practical application of three such fractional mathematical models, which are the time-fractional Klein–Gordon equation (KGE), the time-fractional Sharma–Tasso–Olever equation (STOE), and [...] Read more.
Nonlinear fractional-order differential equations have an important role in various branches of applied science and fractional engineering. This research paper shows the practical application of three such fractional mathematical models, which are the time-fractional Klein–Gordon equation (KGE), the time-fractional Sharma–Tasso–Olever equation (STOE), and the time-fractional Clannish Random Walker’s Parabolic equation (CRWPE). These models were investigated by using an expansion method for extracting new soliton solutions. Two types of results were found: one was trigonometric and the other one was an exponential form. For a profound explanation of the physical phenomena of the studied fractional models, some results were graphed in 2D, 3D, and contour plots by imposing the distinctive results for some parameters under the oblige conditions. From the numerical investigation, it was noticed that the obtained results referred smooth kink-shaped soliton, ant-kink-shaped soliton, bright kink-shaped soliton, singular periodic solution, and multiple singular periodic solutions. The results also showed that the amplitude of the wave augmented with the pulsation in time, which derived the order of time fractional coefficient, remarkably enhanced the wave propagation, and influenced the nonlinearity impacts. Full article
(This article belongs to the Special Issue Recent Advances in Computational Physics with Fractional Application, 2nd Edition)
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19 pages, 1196 KiB  
Article
Fractional Optimal Control Model and Bifurcation Analysis of Human Syncytial Respiratory Virus Transmission Dynamics
by Muath Awadalla, Jihan Alahmadi, Kumama Regassa Cheneke and Sania Qureshi
Fractal Fract. 2024, 8(1), 44; https://doi.org/10.3390/fractalfract8010044 - 11 Jan 2024
Cited by 2 | Viewed by 1138
Abstract
In this paper, the Caputo-based fractional derivative optimal control model is looked at to learn more about how the human respiratory syncytial virus (RSV) spreads. Model solution properties such as boundedness and non-negativity are checked and found to be true. The fundamental reproduction [...] Read more.
In this paper, the Caputo-based fractional derivative optimal control model is looked at to learn more about how the human respiratory syncytial virus (RSV) spreads. Model solution properties such as boundedness and non-negativity are checked and found to be true. The fundamental reproduction number is calculated by using the next-generation matrix’s spectral radius. The fractional optimal control model includes the control functions of vaccination and treatment to illustrate the impact of these interventions on the dynamics of virus transmission. In addition, the order of the derivative in the fractional optimal control problem indicates that encouraging vaccination and treatment early on can slow the spread of RSV. The overall analysis and the simulated behavior of the fractional optimum control model are in good agreement, and this is due in large part to the use of the MATLAB platform. Full article
(This article belongs to the Special Issue Recent Advances in Computational Physics with Fractional Application, 2nd Edition)
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25 pages, 6122 KiB  
Article
Finite Difference Modeling of Time Fractal Impact on Unsteady Magneto-hydrodynamic Darcy–Forchheimer Flow in Non-Newtonian Nanofluids with the q-Derivative
by Amani S. Baazeem, Yasir Nawaz and Muhammad Shoaib Arif
Fractal Fract. 2024, 8(1), 8; https://doi.org/10.3390/fractalfract8010008 - 20 Dec 2023
Viewed by 1032
Abstract
This contribution addresses a fractal numerical scheme that can be employed for handling fractal time-dependent parabolic equations. The numerical scheme presented in this contribution can be used to discretize integer order and fractal derivatives in a given differential equation. Therefore, the scheme and [...] Read more.
This contribution addresses a fractal numerical scheme that can be employed for handling fractal time-dependent parabolic equations. The numerical scheme presented in this contribution can be used to discretize integer order and fractal derivatives in a given differential equation. Therefore, the scheme and results can be used for both cases. The proposed finite difference scheme is based on two stages. Fractal time derivatives are discretized by employing the proposed approach. For the scalar convection–diffusion equation, we derive the stability condition of the proposed fractal scheme. Using a nonlinear chemical reaction, the approach is also used to solve the Quantum Calculus model of a Williamson nanofluid’s unsteady Darcy–Forchheimer flow over flat and oscillatory sheets. The findings indicate a negative correlation between the velocity profile and the porosity parameter and inertia coefficient, with an increase in these factors resulting in a drop in the velocity profile. Additionally, the fractal scheme under consideration is being compared to the fractal Crank–Nicolson method, revealing that the proposed scheme exhibits a superior convergence speed compared to the fractal Crank–Nicolson method. Several problems involving the motion of non-Newtonian nanofluids through magnetic fields and porous media can be investigated with the help of the proposed numerical scheme. This research has implications for developing more efficient heat transfer and energy conversion devices based on nanofluids. Full article
(This article belongs to the Special Issue Recent Advances in Computational Physics with Fractional Application, 2nd Edition)
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19 pages, 3782 KiB  
Article
Multi-Peak and Propagation Behavior of M-Shape Solitons in (2 + 1)-Dimensional Integrable Schwarz-Korteweg-de Vries Problem
by Sarfaraz Ahmed, Aly R. Seadawy, Syed T. R. Rizvi and Umar Raza
Fractal Fract. 2023, 7(10), 709; https://doi.org/10.3390/fractalfract7100709 - 26 Sep 2023
Cited by 3 | Viewed by 787
Abstract
This paper examines the propagation of M-shape solitons and their interactions with kink waves to the (2 + 1)-dimensional integrable Schwarz-Korteweg-de Vries (ISKdV) problem by applying the symbolic computation with ansatz functions technique and logarithmic transformation. The governing model usually appears in [...] Read more.
This paper examines the propagation of M-shape solitons and their interactions with kink waves to the (2 + 1)-dimensional integrable Schwarz-Korteweg-de Vries (ISKdV) problem by applying the symbolic computation with ansatz functions technique and logarithmic transformation. The governing model usually appears in the nonlinear shallow water waves and fluid mechanics. We discuss various nonlinear waves like multiwave solutions (MSs), homoclinic breather (HB), M-shape solitons, single exponential form (one-kink), and double exponential form (two-kink). These waves have lot of applications in fluid dynamics, nonlinear optics, chemical reaction networks, biological systems, climate science, and material science. We also study interaction among M-shape solitons with kink wave. At the end, we discuss the stability characteristics of all solutions. Full article
(This article belongs to the Special Issue Recent Advances in Computational Physics with Fractional Application, 2nd Edition)
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11 pages, 958 KiB  
Article
An Accurate Approach to Simulate the Fractional Delay Differential Equations
by Mohamed Adel, Mohamed M. Khader, Salman Algelany and Khaled Aldwoah
Fractal Fract. 2023, 7(9), 671; https://doi.org/10.3390/fractalfract7090671 - 05 Sep 2023
Cited by 1 | Viewed by 1044
Abstract
The fractional Legendre polynomials (FLPs) that we present as an effective method for solving fractional delay differential equations (FDDEs) are used in this work. The Liouville–Caputo sense is used to characterize fractional derivatives. This method uses the spectral collocation technique based on FLPs. [...] Read more.
The fractional Legendre polynomials (FLPs) that we present as an effective method for solving fractional delay differential equations (FDDEs) are used in this work. The Liouville–Caputo sense is used to characterize fractional derivatives. This method uses the spectral collocation technique based on FLPs. The proposed method converts FDDEs into a set of algebraic equations. We lay out a study of the convergence analysis and figure out the upper bound on error for the approximate solution. Examples are provided to demonstrate the precision of the suggested approach. Full article
(This article belongs to the Special Issue Recent Advances in Computational Physics with Fractional Application, 2nd Edition)
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18 pages, 2433 KiB  
Article
The Effects of Thermal Memory on a Transient MHD Buoyancy-Driven Flow in a Rectangular Channel with Permeable Walls: A Free Convection Flow with a Fractional Thermal Flux
by Nehad Ali Shah, Bander Almutairi, Dumitru Vieru and Ahmed A. El-Deeb
Fractal Fract. 2023, 7(9), 664; https://doi.org/10.3390/fractalfract7090664 - 01 Sep 2023
Viewed by 632
Abstract
This study investigates the effects of magnetic induction, ion slip and Hall current on the flow of linear viscous fluids in a rectangular buoyant channel. In a hydro-magnetic flow scenario with permeable and conducting walls, one wall has a temperature variation that changes [...] Read more.
This study investigates the effects of magnetic induction, ion slip and Hall current on the flow of linear viscous fluids in a rectangular buoyant channel. In a hydro-magnetic flow scenario with permeable and conducting walls, one wall has a temperature variation that changes over time, while the other wall keeps a constant temperature; the research focuses on this situation. Asymmetric wall heating and suction/injection effects are also examined in the study. Using the Laplace transform, analytical solutions in the Laplace domain for temperature, velocity and induced magnetic field have been determined. The Stehfest approach has been used to find numerical solutions in the real domain by reversing Laplace transforms. The generalized thermal process makes use of an original fractional constitutive equation, in which the thermal flux is influenced by the history of temperature gradients, which has an impact on both the thermal process and the fluid’s hydro-magnetic behavior. The influence of thermal memory on heat transfer, fluid movement and magnetic induction was highlighted by comparing the solutions of the fractional model with the classic one based on Fourier’s law. Full article
(This article belongs to the Special Issue Recent Advances in Computational Physics with Fractional Application, 2nd Edition)
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17 pages, 997 KiB  
Article
Analytical Solutions of the Predator–Prey Model with Fractional Derivative Order via Applications of Three Modified Mathematical Methods
by Mounirah Areshi, Aly R. Seadawy, Asghar Ali, Amal F. Alharbi and Abdulrahman F. Aljohani
Fractal Fract. 2023, 7(2), 128; https://doi.org/10.3390/fractalfract7020128 - 30 Jan 2023
Cited by 5 | Viewed by 1406
Abstract
We have investigated wave solutions of the Predator–Prey (PP) model with fractional derivative order by novel three modified mathematical methods with the help of the Mathematica platform. The derived solutions are in the form of distinct functions such as trigonometric, hyperbolic, exponential and [...] Read more.
We have investigated wave solutions of the Predator–Prey (PP) model with fractional derivative order by novel three modified mathematical methods with the help of the Mathematica platform. The derived solutions are in the form of distinct functions such as trigonometric, hyperbolic, exponential and rational functional. For the physical phenomena of fractional model, some solutions are plotted in 2-dimensional and 3-dimensional by inserting specific values to attached parameters under sufficient condition on each solution. Hence, proposed schemes are enormously superbly mathematical tools to review wave solutions of several fractional models in nonlinear science. Full article
(This article belongs to the Special Issue Recent Advances in Computational Physics with Fractional Application, 2nd Edition)
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