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Öğe A Standardized Numerical Methodology and Analysis for the Time Delayed Fractional Epidemic Model of Infectious Illnesses Spread by Lumpy Skin(L and H Scientific Publishing, LLC, 2025-06) Mudassar Rafique; Muhammad Aziz Ur Rehamn; Muhammad Rafiq; Zafar Iqbal; Nauman Ahmed; Ali AkgulThis study aims to investigate the solution of fractional order delayed lumpy skin infection model with Caputo operator numerically as well as analytically. This delay factor helps to control and slow down the spread of infection in individuals. In this study, existence and uniqueness of the underlying model is discussed. Equilibria of the lumpy skin model are computed along with reproductive number (R0), if R0 > 1 refers spread of illness and if R0 < 1 means control of disease. Local and global stability of fraction delayed model is also presented. Moreover, positive and bounded solution of proposed model are investigated. For the numerical solution of this model, we use Grunwald Letnikov non-standard finite difference scheme. The key properties of the numerical scheme are also investigated like positivity and boundedness. Numerical example is given to present the graphical solution of the fractional order delay epidemic model.Öğe Modeling and analyzing the dynamics of brucellosis disease with vaccination in the fractional derivative under real cases(Springer Science and Business Media LLC, 2025-03-21) Bashir Al-Hdaibat; Muhammad Altaf Khan; Irfan Ahmad; Ebraheem Alzahrani; Ali AkgulThe present explores the brucellosis model in non-integer derivative by utilizing the real statistics from the mainland China. The formulation of the model first presented in integer order derivative and subsequently extended to fractional order using the Caputo derivative. The existence and uniqueness of the nonlinear fractional system is confirmed, which is the important requirement for a fractional nonlinear model. The local asymptotical stability of the fractional model when R-0 < 1 is analyzed. When R-0 <= 1, the model is found globally asymptotically stable. The existence of an endemic equilibria is given and found that the model has a unique endemic equilibrium. Using the reported cases of brucellosis in mainland China from 2004 to 2018 are considered. Graphical results for data fitting in cumulative and daily wise are presented with their respective residuals. The basic reproduction number is obtained from data fitting is R-0 = 1.0327. A numerical scheme for the Caputo case is provided in detailed and later the scheme was used to obtain the numerical results graphically. Various results regarding the disease curtail are presented graphically, that will be helpful for the disease elimination in the long run. The public health authority and the health agencies can utilize this work confidently for brucellosis control in mainland China.Öğe New exact soliton wave solutions appear in optical fibers with Sardar sub equation and new auxiliary equation techniques(Springer Science and Business Media LLC, 2025-02-05) Umair Asghar; Muhammad Imran Asjad; Yasser Salah Hamed; Ali Akgul; Murad Khan HassaniThis paper comprehensively analyzes exact solutions for the nonlinear long-short wave interaction system within the optical field. Consider two general techniques in this field, the Sardar sub-equation method, and a new auxiliary-equation technique. These methods are applied to derive a wide range of soliton solutions for nonlinear partial differential equations. By transforming the original partial differential equation into an ordinary differential equation using an appropriate transformation, various types of solitary wave solutions are obtained. The novelty of this work lies in the application of two powerful analytical methods. The study significantly broadens the scope of these techniques and their applications, providing a diverse set of exact solutions. To enhance comprehension, the obtained solutions are visualized through 3D, 2D, contour, and density plots, offering clear insights into the dynamics of solitary waves. Long-short-wave interaction model has many applications in different kinds of areas such as in optical fiber communication, to understand the interaction between different wave components that can influence the transmission of signals. This model is used to study the interaction between ion-acoustic waves and electron plasma waves. This helps in understanding energy transfer and wave stability in plasma, which is essential for applications like fusion energy research and space plasma. This is important in coastal engineering for predicting wave behaviors that affect coastal structures, sediment transport, and tsunami dynamics.Öğe Second order slip micropolar MHD hybrid nanofluid flow over a stretching surface with uniform heat source and activation energy: Numerical computational approach(Elsevier BV, 2025-03) Syed Arshad Abas; Hakeem Ullah; Mehreen Fiza; Ali Akgul; Aasim Ullah Jan; Magda Abd El-Rahman; Seham M. Al-MekhlafiApplications: Micropolar fluids are extensively used in lubrication, polymer processing, and heat transfer applications to enhance performance in systems with suspended microstructures. These fluids find applications in industries such as medical, chemical, and microfluidics. Recent advancements have highlighted the potential of hybrid nanofluids in further improving thermal and flow characteristics. Novelty: Motivated by these developments, this study investigates the heat and mass transfer characteristics of a micropolar hybrid nanofluid comprising titanium dioxide (TiO2) and silver (Ag) nanoparticles suspended in water. The analysis focuses on the effects of slip boundary conditions, Joule heating, thermal radiation, heat sources, magnetohydrodynamic (MHD) effects, activation energy, and binary chemical reactions. Methodology: A mathematical model is formulated based on boundary-layer approximations, leading to a system of partial differential equations (PDEs) that describe the flow, thermal, and concentration fields. These PDEs are subsequently transformed into a set of ordinary differential equations (ODEs) using similarity transformations. The resulting higher-order nonlinear ODEs are solved numerically using the bvp4c technique in MATLAB. Findings: The results reveal that the inclusion of slip boundary conditions significantly influences the flow dynamics, reducing skin friction by 4.9 % and 10.4 % with increasing magnetic and material parameters, respectively, but enhancing it with a higher slip factor by 18.88 %. Additionally, an increased volume fraction of nanoparticles elevates the heat transfer rate by 6.3 % while diminishing the Sherwood number by 2.6 %, showcasing the thermal enhancement capabilities of the hybrid nanofluid. This study contributes to the field by providing new insights into the combined effects of Joule heating, activation energy, and chemical reactions on micropolar hybrid nanofluid flow. The result of bvp4c compared with previous literature and found to be closely aligned with published work. The findings have implications for the optimization of thermal management systems and processes in advanced engineering and industrial applications.Öğe Thermal radiation effects of ternary hybrid nanofluid flow in the activation energy: Numerical computational approach(Elsevier BV, 2025-03) Hakeem Ullah; Syed Arshad Abas; Mehreen Fiza; Aasim Ullah Jan; Ali Akgul; Magda Abd El-Rahman; Seham M. Al-MekhlafiSignificance: The remarkable thermal conductivity and heat transfer characteristics of nanofluids make them extremely valuable in thermal engineering and other areas. Due to their increased effectiveness, nanofluids are incredibly useful for improving the efficiency of cooling systems, heating processes, and thermal management applications. Rotating machinery and gas turbine rotators are some industrial applications of hybrid nanofluids as heat transport fluids. Purpose: This study introduces a novel investigation into heat transport phenomena of ternary hybrid, hybrid and nanofluid containing copper, silver and alumina nanoparticles within two stretchy rotating disks maintaining a constant distance. The analysis incorporates the effects of thermal radiation, heat source, joule heating, and Arrhenius activation energy into the equations to stabilize the new composition's flow and thermal properties. Methodology: After utilizing von Karman similarity transformations to renovate the principal equations into the set of nonlinear differential equation systems, the resulting equations were solved using the bvp4c numerical approach with the assistance of MATLAB software. Findings: Graphs are used to explain the results in three different kinds of flows: hybrid fluid (Cu+Al2O3/H2O), nanofluid (Cu/H2O), and ternary hybrid fluid (Cu+Al2O3+Ag/H2O). Additionally, the outcomes of the variable parameters are presented and briefly discussed for different flow profiles. There is encouraging evidence that the numerical code for this study is compatible with previously published work. The skin friction improves 5 % due to the higher values of magnetic and stretching parameter at lower disk. The rate of the heat transfer improved 28 % for ternary nanoparticles as compared to hybrid and single nanofluids. Sherwood's number exhibits both growing and decreasing behaviors for Schmidt and Reynolds’ numbers. All the involved factors enhances the temperature profile. The radiation parameter boost the Nusselt number for ternary hybrid nanofluid up to 6 % and 3.4 % at lower and upper disk as compare to nanofluid.
