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(searched for: doi:10.53391/mmnsa.2022.01.002)
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Yassine Sabbar, , Nadia Gul, Driss Kiouach, S. P. Rajasekar, Nasim Ullah, Alsharef Mohammad
Aims Mathematics, Volume 8, pp 1329-1344; https://doi.org/10.3934/math.2023066

Abstract:
Exhaustive surveys have been previously done on the long-time behavior of illness systems with Lévy motion. All of these works have considered a Lévy–Itô decomposition associated with independent white noises and a specific Lévy measure. This setting is very particular and ignores an important class of dependent Lévy noises with a general infinite measure (finite or infinite). In this paper, we adopt this general framework and we treat a novel correlated stochastic $ SIR_p $ system. By presuming some assumptions, we demonstrate the ergodic characteristic of our system. To numerically probe the advantage of our proposed framework, we implement Rosinski's algorithm for tempered stable distributions. We conclude that tempered tails have a strong effect on the long-term dynamics of the system and abruptly alter its behavior.
Published: 10 October 2022
by MDPI
Fractal and Fractional, Volume 6; https://doi.org/10.3390/fractalfract6100580

Abstract:
The Navier–Stokes (NS) equations involving MHD effects with time-fractional derivatives are discussed in this paper. This paper investigates the local and global existence and uniqueness of the mild solution to the NS equations for the time fractional differential operator. In addition, we work on the regularity effects of such types of equations which are caused by MHD flow.
Eltaib M Abd Elmohmoud,
Published: 12 September 2022
Journal of Taibah University for Science, Volume 16, pp 774-787; https://doi.org/10.1080/16583655.2022.2119738

Abstract:
This study solves systems of partial differential equations with fractional-order derivatives using a modified decomposition approach. Fractional-order derivatives are expressed using the Caputo operator. The validity of the suggested technique is tested using illustrative cases. The exact and Elzaki Adomian decomposition method (EADM) solutions were in close proximity, according to the solution graphs. The suggested strategy’s dependability is shown by the fact that fractional-order problems tend to converge on the solution to an integer-order problem. The present approach may be utilized to answer a broad variety of fractional-order issues since it is more precise and simple to use. Finally, some examples show how the new strategy is uncomplicated, effective, and precise. The approximate solutions have also been displayed at the conclusion of this study.
William Atokolo, Remigius Okeke Aja, Stephen Ekwueme Aniaku, Ifeanyi Sunday Onah, Godwin C. E. Mbah
International Journal of Mathematics and Mathematical Sciences, Volume 2022, pp 1-24; https://doi.org/10.1155/2022/2297630

Abstract:
Sterile insect technology (SIT) is an environmental-friendly method which depends on the release of sterile male mosquitoes that compete with the wild male mosquitoes and mate with wild female mosquitoes, which leads to the production of no offspring and as such reduces the population of Zika virus vector population over time, thereby eliminating the spread of Zika virus in a population. The fractional order sterile insect technology (SIT) model to reduce the spread of Zika virus disease is considered in this present work. We employed the use Laplace–Adomian decomposition method (LADM) to determine an analytical (approximate) solution of the model. The Laplace–Adomian decomposition method (LADM) produced a solution in form of an infinite series that further converges to the exact value. We compared solutions of the fractional model with the classical case using our plots and discovered that the fractional order has more degree of freedom and as such the system can be varied to get many preferred responses of the different classes of the model as the fraction (β) could be varied to the desired rate, say 0.7, 0.4, etc. We have been able to show that LADM can be used to solve an SIT model which has never been done before in literature.
Published: 11 July 2022
by MDPI
Mathematical and Computational Applications, Volume 27; https://doi.org/10.3390/mca27040058

Abstract:
The present research was developed to find out the effect of heated cylinder configurations in accordance with the magnetic field on the natural convective flow within a square cavity. In the cavity, four types of configurations—left bottom heated cylinder (LBC), right bottom heated cylinder (RBC), left top heated cylinder (LTC) and right top heated cylinder (RTC)—were considered in the investigation. The current mathematical problem was formulated using the non-linear governing equations and then solved by engaging the process of Galerkin weighted residuals based on the finite element scheme (FES). The investigation of the present problem was conducted using numerous parameters: the Rayleigh number (Ra = 103–105), the Hartmann number (Ha = 0–200) at Pr = 0.71 on the flow field, thermal pattern and the variation of heat inside the enclosure. The clarifications of the numerical result were exhibited in the form of streamlines, isotherms, velocity profiles and temperature profiles, local and mean Nusselt number, along with heated cylinder configurations. From the obtained outcomes, it was observed that the rate of heat transport, as well as the local Nusselt number, decreased for the LBC and LTC configurations, but increased for the RBC and RTC configurations with the increase of the Hartmann number within the square cavity. In addition, the mean Nusselt number for the LBC, RBC, LTC and RTC configurations increased when the Hartmann number was absent, but decreased when the Hartmann number increased in the cavity. The computational results were verified in relation to a published work and were found to be in good agreement.
Published: 11 June 2022
Advances in Mathematical Physics, Volume 2022, pp 1-17; https://doi.org/10.1155/2022/4552179

Abstract:
The conformable fractional triple Laplace transform approach, in conjunction with the new Iterative method, is used to examine the exact analytical solutions of the (2 + 1)-dimensional nonlinear conformable fractional Telegraph equation. All the fractional derivatives are in a conformable sense. Some basic properties and theorems for conformable triple Laplace transform are presented and proved. The linear part of the considered problem is solved using the conformable fractional triple Laplace transform method, while the noise terms of the nonlinear part of the equation are removed using the novel Iterative method’s consecutive iteration procedure, and a single iteration yields the exact solution. As a result, the proposed method has the benefit of giving an exact solution that can be applied analytically to the presented issues. To confirm the performance, correctness, and efficiency of the provided technique, two test modeling problems from mathematical physics, nonlinear conformable fractional Telegraph equations, are used. According to the findings, the proposed method is being used to solve additional forms of nonlinear fractional partial differential equation systems. Moreover, the conformable fractional triple Laplace transform iterative method has a small computational size as compared to other methods.
Published: 26 May 2022
by MDPI
Mathematical and Computational Applications, Volume 27; https://doi.org/10.3390/mca27030046

Abstract:
This article aims to develop a mathematical simulation of the steady mixed convective Darcy–Forchheimer flow of Williamson nanofluid over a linear stretchable surface. In addition, the effects of Cattaneo–Christov heat and mass flux, Brownian motion, activation energy, and thermophoresis are also studied. The novel aspect of this study is that it incorporates thermal radiation to investigate the physical effects of thermal and solutal stratification on mixed convection flow and heat transfer. First, the profiles of velocity and energy equations were transformed toward the ordinary differential equation using the appropriate similarity transformation. Then, the system of equations was modified by first-order ODEs in MATLAB and solved using the bvp4c approach. Graphs and tables imply the impact of physical parameters on concentration, temperature, velocity, skin friction coefficient, mass, and heat transfer rate. The outcomes show that the nanofluid temperature and concentration are reduced with the more significant thermal and mass stratification parameters estimation.
Published: 10 May 2022
by MDPI
Fractal and Fractional, Volume 6; https://doi.org/10.3390/fractalfract6050263

Abstract:
A novel computational approach is developed to investigate the mixed convection, boundary layer flow over a nonlinear elastic (stretching or shrinking) surface. The viscous fluid is electrically conducting, incompressible, and propagating through a porous medium. The consequences of viscous dissipation, Joule heating, and heat sink/source of the volumetric rate of heat generation are also included in the energy balance equation. In order to formulate the mathematical modeling, a similarity analysis is performed. The numerical solution of nonlinear differential equations is accomplished through the use of a robust computational approach, which is identified as the Spectral Local Linearization Method (SLLM). The computational findings reported in this study show that, in addition to being simple to establish and numerically implement, the proposed method is very reliable in that it converges rapidly to achieve a specified goal and is more effective in resolving very complex models of nonlinear boundary value problems. In order to ensure the convergence of the proposed SLLM method, the Gauss–Seidel approach is used. The SLLM’s reliability and numerical stability can be optimized even more using Gauss–Seidel approach. The computational results for different emerging parameters are computed to show the behavior of velocity profile, skin friction coefficient, temperature profile, and Nusselt number. To evaluate the accuracy and the convergence of the obtained results, a comparison between the proposed approach and the bvp4c (built-in command in Matlab) method is presented. The Matlab software, which is used to generate machine time for executing the SLLM code, is also displayed in a table.
Published: 1 April 2022
by MDPI
Journal: Mathematics
Mathematics, Volume 10; https://doi.org/10.3390/math10071125

Abstract:
This work proposes a qualitative study for the fractional second-grade fluid described by a fractional operator. The classical Caputo fractional operator is used in the investigations. The exact analytical solutions of the constructed problems for the proposed model are determined by using the Laplace transform method, which particularly includes the Laplace transform of the Caputo derivative. The impact of the used fractional operator is presented; especially, the acceleration effect is noticed in the paper. The parameters’ influences are focused on the dynamics such as the Prandtl number (Pr), the Grashof numbers (Gr), and the parameter η when the fractional-order derivative is used in modeling the second-grade fluid model. Their impacts are also analyzed from a physical point of view besides mathematical calculations. The impact of the fractional parameter α is also provided. Finally, it is concluded that the graphical representations support the theoretical observations of the paper.
Published: 11 February 2022
by MDPI
Fractal and Fractional, Volume 6; https://doi.org/10.3390/fractalfract6020101

Abstract:
In this article, unsteady free convective heat transport of copper-water nanofluid within a square-shaped enclosure with the dominance of non-uniform horizontal periodic magnetic effect is investigated numerically. Various nanofluids are also used to investigate temperature performance. The Brownian movement of nano-sized particles is included in the present model. A sinusoidal function of the y coordinate is considered for the magnetic effect, which works as a non-uniform magnetic field. The left sidewall is warmed at a higher heat, whereas the right sidewall is cooled at a lower heat. The upper and bottom walls are insulated. For solving the governing non-linear partial differential equation, Galerkin weighted residual finite element method is devoted. Comparisons are made with previously published articles, and we found there to be excellent compliance. The influence of various physical parameters, namely, the volume fraction of nanoparticles, period of the non-uniform magnetic field, Rayleigh number, the shape and diameter of nanoparticles, and Hartmann number on the temperature transport and fluid flow are researched. The local and average Nusselt number is also calculated to investigate the impact of different parameters on the flow field. The results show the best performance of heat transport for the Fe3O4-water nanofluid than for other types of nanofluids. The heat transport rate increases 20.14% for Fe3O4-water nanofluid and 8.94% for TiO2-water nanofluid with 1% nanoparticles volume. The heat transportation rate enhances with additional nanoparticles into the base fluid whereas it decreases with the increase of Hartmann number and diameter of particles. A comparison study of uniform and non-uniform magnetic effects is performed, and a higher heat transfer rate is observed for a non-uniform magnetic effect compared to a uniform magnetic effect. Moreover, periods of magnetic effect and a nanoparticle’s Brownian movement significantly impacts the temperature transport and fluid flow. The solution reaches unsteady state to steady state within a very short time.
Hassan Khan, Hajira, Qasim Khan, Poom Kumam, Fairouz Tchier, Gurpreet Singh, Kanokwan Sitthithakerngkiet, Ferdous Mohammed Tawfiq
Published: 1 January 2022
Journal: Open Physics
Open Physics, Volume 20, pp 764-777; https://doi.org/10.1515/phys-2022-0072

Abstract:
Usually, to find the analytical and numerical solution of the boundary value problems of fractional partial differential equations is not an easy task; however, the researchers devoted their sincere attempt to find the solutions of various equations by using either analytical or numerical procedures. In this article, a very accurate and prominent method is developed to find the analytical solution of hyperbolic-telegraph equations with initial and boundary conditions within the Caputo operator, which has very simple calculations. This method is called a new technique of Adomian decomposition method. The obtained results are described by plots to confirm the accuracy of the suggested technique. Plots are drawn for both fractional and integer order solutions to confirm the accuracy and validity of the proposed method. Solutions are obtained at different fractional orders to discuss the useful dynamics of the targeted problems. Moreover, the suggested technique has provided the highest accuracy with a small number of calculations. The suggested technique gives results in the form of a series of solutions with easily computable and convergent components. The method is simple and straightforward and therefore preferred for the solutions of other problems with both initial and boundary conditions.
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