A fractional-order model of COVID-19 and human Metapneumovirus co-dynamics: a Laplace-Adomian decomposition approach for epidemiological prediction and intervention analysis, 2025
to critical respiratory problems and organ dysfunction [2]. Due to its rapid global transmission ... more to critical respiratory problems and organ dysfunction [2]. Due to its rapid global transmission and high death toll, the World Health Organization declared it a pandemic in March 2020 [3]. In response, governments and health organizations introduced various measures such as lockdown, social distancing, wearing face masks in public places, and mass vaccination programs to curb the virus's spread [4]. On the other hand, human Metapneumovirus (HMPV) [5] has also emerged as a threat. Although it was first identified in the Netherlands in 2001, its symptoms are similar to those of COVID-19, but the vaccine has not yet been developed [6]. HMPV is a member of the Paramyxoviridae family and causes respiratory infections such as cough, shortness of breath, bronchitis, and pneumonia [7]. Studies have shown that HMPV affects mainly infants, young children, and the elderly, and most HMPV-positive individuals have no preexisting health conditions [8]. It is challenging to accurately diagnose due to the lack of specific treatment or symptoms [9]. Since the symptoms of COVID-19 and HMPV are very similar, there is a strong possibility that both infections can coexist in the same individual, potentially complicating M. S. Osman
In this study, the double (G /G, 1/G)-expansion method is utilized for illustrating the improved ... more In this study, the double (G /G, 1/G)-expansion method is utilized for illustrating the improved explicit integral solutions for the two of nonlinear evolution equations. To expose the importance and convenience of our assumed method, we herein presume two models, namely the nano-ionic currents equation and the soliton equation. The exact solutions are generated with the aid of our proposed method in such a manner that the solutions involve to the rational, trigonometric, and hyperbolic functions for the first presumed nonlinear equation as well as the trigonometric and hyperbolic functions for the second one with meaningful symbols that promote some unique periodic and solitary solutions. The method used here is an extension of the (G /G)-expansion method to rediscover all known solutions. We offer 2D and 3D charts of the various recovery solutions to better highlight our findings. Finally, we compared our results with those of earlier solutions.
In this work, a new adaptive numerical method is proposed for solving nonlinear, singular, and st... more In this work, a new adaptive numerical method is proposed for solving nonlinear, singular, and stiff initial value problems often encountered in real life. Starting with a fixed step size, the new method's performance can be significantly enhanced by introducing an adaptive step-size approach. The qualitative properties of the proposed method have been investigated to determine the efficiency and reliability of the method. The proposed method is of fifth-order accuracy, zero stable, L-stable, and consistent. In addition, the proposed method is convergent, and its stability properties are also shown through its Order Stars. Finally, numerical experiments are conducted to illustrate the performance of the method. The results obtained show that the proposed method compares favourably with existing methods.
In this work, a new adaptive numerical method is proposed for solving nonlinear, singular, and st... more In this work, a new adaptive numerical method is proposed for solving nonlinear, singular, and stiff initial value problems often encountered in real life. Starting with a fixed step size, the new method's performance can be significantly enhanced by introducing an adaptive step-size approach. The qualitative properties of the proposed method have been investigated to determine the efficiency and reliability of the method. The proposed method is of fifth-order accuracy, zero stable, L-stable, and consistent. In addition, the proposed method is convergent, and its stability properties are also shown through its Order Stars. Finally, numerical experiments are conducted to illustrate the performance of the method. The results obtained show that the proposed method compares favourably with existing methods.
Lump solutions are a prominent option for numerous models of nonlinear evolution. The intention o... more Lump solutions are a prominent option for numerous models of nonlinear evolution. The intention of this research is to explore the variable coefficients Kadomtsev-Petviashvili equation. We auspiciously provide multiple soliton and M-lump solutions to this equation. Additionally, the presented results are also supplied with collision phenomena. Owing of its essential role, we employ appropriate parameter values to emphasis the physical characteristics of the provided results using 3D and contour charts. The outcomes of this work convey the physical characteristics of lump and lump interactions that occur in many dynamical regimes.
In this study, we express the Radhakrishnan-Kundu-Lakshmanan equation with an arbitrary index of ... more In this study, we express the Radhakrishnan-Kundu-Lakshmanan equation with an arbitrary index of n ∈ Q. We investigated the solitary wave solutions of the Radhakrishnan-Kundu-Lakshmanan equation by mean of the Jacobi elliptic function expansion technique. As a result, we constructed several distinct solutions include dark, bright, singular, periodic, hyperbolic, trigonometric, and Jacobi elliptic function types solutions. To highlight the dynamic behavior of the generated solutions, specific values for the parameters are also assigned. The above techniques could also be employed to get a variety of exact solutions for other nonlinear models in physics, applied mathematics, and engineering.
To generate different optical soliton solutions of the Paraxial wave equation with fractional tim... more To generate different optical soliton solutions of the Paraxial wave equation with fractional time dependence, a well-known Sardar-subequation technique is used. The M-truncated fractional derivative is used to get rid of the fractional order in the governing model equation. The sorts of wave solutions acquired have important applications in engineering and material science. Some particular values of the parameters have been selected in order to produce creative solitary wave solutions. The obtained wave solutions are displayed graphically using Maple.
The applications of the diffusion wave model of a time-fractional kind with damping and reaction ... more The applications of the diffusion wave model of a time-fractional kind with damping and reaction terms can occur within classical physics. This quantification of the activity can measure the diagnosis of mechanical waves and light waves. The goal of this work is to predict and construct numerical solutions for such a diffusion model based on the uniform cubic B-spline functions. The Caputo time-fractional derivative has been estimated using the standard finite difference technique, whilst, the uniform cubic B-spline functions have been employed to achieve spatial discretization. The convergence of the suggested blueprint is discussed in detail. To assert the efficiency and authenticity of the study, we compute the approximate solutions for a couple of applications of the diffusion model in electromagnetics and fluid dynamics. To show the mathematical simulation, several tables and graphs are shown, and it was found that the graphical representations and their physical explanations describe the behavior of the solutions lucidly. The key benefit of the resultant scheme is that the algorithm is straightforward and makes it simple to implement as utilized in the highlight and conclusion part.
Our work aims to investigate the vcBLMPE in (3 + 1)-dimensions (3D-vcBLMPE) that characterizes wa... more Our work aims to investigate the vcBLMPE in (3 + 1)-dimensions (3D-vcBLMPE) that characterizes wave propagation in incompressible fluids. In real-world issues, nonlinear partial differential equations containing time-dependent coefficients are more relevant than those with constant coefficients owing to inhomogeneities of media and nonuniformities of boundaries. In shallow water, linearization of the wave formation needs more critical wave capacity criteria than in water depths, and the strongly nonlinear aspects are readily visible. By using symbolic computation, several nonautonomous wave solutions with different geometric structures are obtained. Each of the gained solutions is presented graphically based on various arbitrary coefficients to demonstrate and better com
Our work aims to investigate the vcBLMPE in (3 + 1)-dimensions (3D-vcBLMPE) that characterizes wa... more Our work aims to investigate the vcBLMPE in (3 + 1)-dimensions (3D-vcBLMPE) that characterizes wave propagation in incompressible fluids. In real-world issues, nonlinear partial differential equations containing time-dependent coefficients are more relevant than those with constant coefficients owing to inhomogeneities of media and nonuniformities of boundaries. In shallow water, linearization of the wave formation needs more critical wave capacity criteria than in water depths, and the strongly nonlinear aspects are readily visible. By using symbolic computation, several nonautonomous wave solutions with different geometric structures are obtained. Each of the gained solutions is presented graphically based on various arbitrary coefficients to demonstrate and better com
In nonlinear optics, photonics, plasma, condensed matter physics, and other domains, the space-ti... more In nonlinear optics, photonics, plasma, condensed matter physics, and other domains, the space-time fractional nonlinear Fokas-Lenells and paraxial Schrödinger equations associated with beta derivative have significant applications. The fractional wave transformation has been used to turn the space-time fractional nonlinear equations into integer order equations. To obtain optical soliton solutions relating to exponential, trigonometric, and hyperbolic functions and their integration with free parameters, the improved Bernoulli sub-equation function (IBSEF) scheme has been exploited. Different shapes of solitons have been extracted from the attained solutions, including kink, periodic, bell-shaped, antikink, dark-bright soliton, single kink type soliton, etc. A kink soliton is an optical shock front that keeps its shape while traveling through optical fibers. The characteristics of the solitons have been studied by describing profiles in 3D, 2D, contour, and density plots. The results imply that the IBSEF technique is simple, efficient, and capable of generating comprehensive soliton solutions of nonlinear models related to telecommunication and optics.
In this paper, we studied the Drinfel'd-Sokolov-Wilson equation (DSWE) and Boiti Leon Pempinelli ... more In this paper, we studied the Drinfel'd-Sokolov-Wilson equation (DSWE) and Boiti Leon Pempinelli equation (BLPE) in the conformable sense. The sine-cosine method is utilized to achieve various traveling wave solutions to the suggested nonlinear systems. It is an easy approach to use and does not require sophisticated mathematical software or a knowledgeable coder. It can also be used for various linear and nonlinear fractional issues, making it pervasive. The obtained solutions in the form of solitons emerge with the necessary constraints to ensure their existence. The obtained results hold significant role in elucidating some important nonlinear problems in applied sciences and engineering.
In this analysis, we use the high order cubic B-spline method to create approximating polynomial ... more In this analysis, we use the high order cubic B-spline method to create approximating polynomial solutions for fractional Painleve´and Bagley-Torvik equations in the Captuo, Caputo-Fabrizio, and conformable fractional sense concerning boundary set conditions. Using a piecewise spline of a 3rd-degree polynomial; the discretization of the utilized fractional model problems is gained. Taking advantage of the Taylor series expansion; the error order behavior spline theorem is proved. We demonstrate applications of our spline method to several certain kinds including the 1st(2nd) Painleve´and Bagley-Torvik fractional models. For more detail, using Mathematica 11 several drawings and many tables were calculated and their explanations were men
The purpose of this work is to seek various innovative exact solutions using the new Kudryashov a... more The purpose of this work is to seek various innovative exact solutions using the new Kudryashov approach to the nonlinear partial differential equations (NLPDEs). This technique obtains novel exact solutions of soliton types. Moreover, several 3D and 2D plots of the higher dimensional Klein-Gordon, Kadomtsev-Petviashvili, and Boussinesq equations are demonstrated by considering the relevant values of the aforementioned parameters to exhibit the nonlinear wave structures more adequately. The new Kudryashov technique is an effective, and simple technique that provides new generalized solitonic wave profiles. It is anticipated that these novel solutions will enable a thorough understanding of the development and dynamic nature of such models.
For uni-directional wave transmission in the smooth bottom of shallow sea water and the supercond... more For uni-directional wave transmission in the smooth bottom of shallow sea water and the superconductivity of nonlinear media with dispersion systems, the (1 + 1)-dimensional Camassa-Holm and Landau-Ginzburg-Higgs equations are of particular interest in research to the academics. Analytical wave solutions to the stated models have been successfully constructed in this study, which might have considerable implications in describing the nonlinear dynamical behavior associated with the phenomena. The models we aim to uncover have been put into the form of differential equations with one characteristic variable expending the wave transformation coordinate and, thereupon, the rational (G ′ /G)-expansion technique is executed. Using the considered technique, diverse soliton solutions in suitable forms arrayed to trigonometric, rational, and hyperbolic functions have been determined. The achieved solutions are figured out in 3D profiles, assigning the free parameters involved in solutions to particular values and discussed their physical significance to bring out the inner context of the tangible incidents in the natural domain. The rational (G ′ /G)-expansion approach is efficient, concise, and capable of finding analytical solutions to other nonlinear models that can be considered in subsequent studies.
In this work, we perform a comprehensive analytical study to find the novel exact traveling wave ... more In this work, we perform a comprehensive analytical study to find the novel exact traveling wave solutions of the (2 + 1)-dimensional Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equation. The recently developed (𝐺′/𝐺′+𝐺+𝐴)-expansion technique is a capable method for finding the new exact solutions of assorted nonlinear evolution equations. Some new analytical solutions are obtained by utilizing the forementioned method. The obtained solutions are expressed as trigonometric functions and exponential functions. The extracted exact wave solutions are advanced and fully unique from the earlier literature Moreover, we have presented the contour simulations, 2D and 3D graphical representations of the solution functions and we have observed that the solutions obtained are periodic and solitary wave solutions. We have shown two soliton wave solutions and two singular periodic wave solutions for the particular values of the parameters graphically. As per our knowledge, we must say that the extracted solutions might be significant and essential for new physical phenomenon.
Uses of the TFDWM in its singular case with damping-reaction terms are widely seen in classical p... more Uses of the TFDWM in its singular case with damping-reaction terms are widely seen in classical physics applications. As the quantitative measurement of activity diagnoses light-mechanical waves resulting from many physical experiments. The goal and importance of this article are to predict and build accurate and convincing numerical solutions for the TFDWM in its singular version by employing the collective CUBSA and SFDA. The FCTD has been estimated and dismantled using the SFDT, whilst, the standard splines will utilize upon realizing spatial discretization. To study the prediction error of our approach some convergence and bound results are given under certain constraints. We demonstrate applications of our collective algorithm to a couple of fractional singular types models appearing in fluid dynamics and electromagnetics. Details analysis, delegate tables, and representative graphs are displayed and offered in different dimensions to handle the crossover meaning for several order values of FCTDs. Some conclusions, observations, recommendations, and future issues were briefly raised in the final section of the letter.
Uses of the TFDWM in its singular case with damping-reaction terms are widely seen in classical p... more Uses of the TFDWM in its singular case with damping-reaction terms are widely seen in classical physics applications. As the quantitative measurement of activity diagnoses light-mechanical waves resulting from many physical experiments. The goal and importance of this article are to predict and build accurate and convincing numerical solutions for the TFDWM in its singular version by employing the collective CUBSA and SFDA. The FCTD has been estimated and dismantled using the SFDT, whilst, the standard splines will utilize upon realizing spatial discretization. To study the prediction error of our approach some convergence and bound results are given under certain constraints. We demonstrate applications of our collective algorithm to a couple of fractional singular types models appearing in fluid dynamics and electromagnetics. Details analysis, delegate tables, and representative graphs are displayed and offered in different dimensions to handle the crossover meaning for several order values of FCTDs. Some conclusions, observations, recommendations, and future issues were briefly raised in the final section of the letter.
The two-dimensional nonlinear complex coupled Maccari system is a significant model in optics, qu... more The two-dimensional nonlinear complex coupled Maccari system is a significant model in optics, quantum mechanics, plasma physics, hydrodynamics and some other fields. In this article, we have investigated scores of broad-spectral soliton solutions to the stated system via the auxiliary equation technique. The obtained solutions are established as an integration of the rational function, hyperbolic function, trigonometric function and exponential function. We have portrayed the three-and two-dimensional combined structures of the obtained solutions for a better interpretation of the waves, and it is determined that is the most effective and influential parameter that significantly affects the change in wave type, as shown in the 2D figure. The effects of other parameters have also been discussed. The numerical results show that the approach is reliable, straightforward and potent to examine other nonlinear evolution equations that emerged in optics, nonlinear physics, applied mathematics, and engineering.
The perturbed nonlinear Schrödinger (NLS) equation and the nonlinear radial dislocations model in... more The perturbed nonlinear Schrödinger (NLS) equation and the nonlinear radial dislocations model in microtubules (MTs) are the underlying frameworks to simulate the dynamic features of solitons in optical fibers and the functional aspects of microtubule dynamics. The generalized Kudryashov method is used in this article to extract stable, generic, and wide-ranging soliton solutions, comprising hyperbolic, exponential, trigonometric, and some other functions, and retrieve diverse known soliton structures by balancing the effects of nonlinearity and dispersion. It is established by analysis and graphs that changing the included parameters changes the waveform behavior, which is largely controlled by nonlinearity and dispersion effects. The impact of the other parameters on the wave profile, such as wave speed, wavenumber, etc., has also been covered. The results obtained demonstrate the reliability, efficiency, and capability of the implemented technique to determine wide-spectral stable soliton solutions to nonlinear evolution equations emerging in various branches of scientific, technological, and engineering domains.
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Papers by Mohammed Safaa
advanced and fully unique from the earlier literature Moreover, we have presented the contour simulations, 2D and 3D graphical representations of the solution functions and we have observed that the solutions obtained are periodic and solitary wave solutions. We have shown two
soliton wave solutions and two singular periodic wave solutions for the particular values of the parameters graphically. As per our knowledge, we must say that the extracted solutions might be significant and essential for new physical phenomenon.