Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 2An Improved Shooting Technique for Solving Boundary Value Problems Using Higher Order Initial Approximation Algorithms(Univ Punjab, dept Mathematics, 2019) Javeed, Shumaila; Baleanu, Dumitru; Shabnum, Assiya; Baleanu, Dumitru; MatematikThis paper introduces the better algorithms to obtain refined initial guesses with shooting method for solving boundary value problems (BVPs). Each boundary value problem (BVP) is reformulated as a system of equations i.e. initial value problems (IVPs) with one unknown initial conditions. Afterwards, the system of equations is solved using newly developed shooting method [2]. This article proposes efficient initial guess algorithms rather than conventional Newton method to approach the adjoint terminal conditions rapidly. We enhanced the efficiency and accuracy of shooting method by first improving our initial guess and then solving the problem iteratively. The suggested technique is applied to solve different nonlinear higher order boundary value problems. The results indicate that the proposed method is more efficient and accurate as compared to build-in-functions which is being used in MATLAB.Article Citation - WoS: 10Citation - Scopus: 10Solitons of the (1+1)- and (2+1)-Dimensional Chiral Nonlinear Schrodinger Equations With the Jacobi Elliptical Function Method(Springer Basel Ag, 2023) Rezazadeh, Hadi; Javeed, Shumaila; Baleanu, Dumitru; Korkmaz, Alper; Tala-Tebue, EricOur objective is to find new analytical solutions of the (1+1)- and (2+1)-dimensional Chiral nonlinear Schrodinger (CNLS) equations using the Jacobi elliptical function method. The CNLS equations play a significant role in the development of quantum mechanics, particularly in the field of quantum Hall effect. Soliton solutions of the considered models are obtained such as, cnoidal solutions, the hyperbolic solutions and the trigonometric solutions. The obtained analytical solutions are new in the literature. The stability conditions of these solutions are also given. The obtained stable solutions are presented graphically for some specific parameters. Moreover, the conditions of modulational instability for both models are provided. The proposed method can be useful to obtain the analytical solutions of nonlinear partial differential equations.Article Citation - WoS: 8Citation - Scopus: 7A Novel Fractional Dengue Transmission Model in the Presence of Wolbachia Using Stochastic Based Artificial Neural Network(Tech Science Press, 2024) Ahmed, Iftikhar; Baleanu, Dumitru; Javeed, Shumaila; Faiz, ZeshanThe purpose of this research work is to investigate the numerical solutions of the fractional dengue transmission model (FDTM) in the presence of Wolbachia using the stochastic-based Levenberg-Marquardt neural network (LM-NN) technique. The fractional dengue transmission model (FDTM) consists of 12 compartments. The human population is divided into four compartments; susceptible humans (Sh), exposed humans (Eh), infectious humans (Ih), and recovered humans (Rh). Wolbachia-infected and Wolbachia-uninfected mosquito population is also divided into four compartments: aquatic (eggs, larvae, pupae), susceptible, exposed, and infectious. We investigated three different cases of vertical transmission probability (77), namely when Wolbachia-free mosquitoes persist only (77 = 0.6), when both types of mosquitoes persist (77 = 0.8), and when Wolbachia-carrying mosquitoes persist only (77 = 1). The objective of this study is to investigate the effectiveness of Wolbachia in reducing dengue and presenting the numerical results by using the stochastic structure LM-NN approach with 10 hidden layers of neurons for three different cases of the fractional order derivatives (alpha = 0.4, 0.6, 0.8). LM-NN approach includes a training, validation, and testing procedure to minimize the mean square error (MSE) values using the reference dataset (obtained by solving the model using the Adams-Bashforth-Moulton method (ABM). The distribution of data is 80% data for training, 10% for validation, and, 10% for testing purpose) results. A comprehensive investigation is accessible to observe the competence, precision, capacity, and efficiency of the suggested LM-NN approach by executing the MSE, state transitions findings, and regression analysis. The effectiveness of the LM-NN approach for solving the FDTM is demonstrated by the overlap of the findings with trustworthy measures, which achieves a precision of up to 10-4.Article Citation - WoS: 2Citation - Scopus: 2Study of Electro-Osmotic Nanofluid Transport for Scraped Surface Heat Exchanger With Heat Transfer Phenomenon(Vinca inst Nuclear Sci, 2021) Imran, Ali; Javeed, Shumaila; Baleanu, Dumitru; Zeb, Muhammad; Ahmad, Sohail; Waheed, AsifIn this study a novel mathematical model for electroosmotic flow for Cu-water based nanofluid with heat transfer phenomenon is reported for scraped-surface heat exchanger. The flow is initiated due to motion of lower wall of the channel and axial pressure gradient. The flow is modelled with aid of low Reynolds number and lubrication approximation theory. Exact analytical expressions are gathered for axial velocity, and stream functions for various stations of scraped-surface heat exchanger. Physical phenomenon of electro osmotic parameter are investigated on velocity profile, velocity distribution and pressure rise at edge of the blades. It is reported that electro-osmotic parameter mainly works as dragging force, it can be used to control the flow. This controlling mechanism may be helpful in mixing different materials in scraped-surface heat exchanger. Pressure rise at edge of the blades mainly rises below the blades with electro-osmotic, whereas, this profiles is suppressed for region above the blades and between the blades.Article Citation - WoS: 11Citation - Scopus: 10Investigation of Electroosmosis Flow of Copper Nanoparticles With Heat Transfer Due To Metachronal Rhythm(Vinca inst Nuclear Sci, 2021) Waheed, Asif; Javeed, Shumaila; Baleanu, Dumitru; Zeb, Muhammad; Ahmad, Sohail; Imran, AliA mathematical model is explored to establish the electroosmotic flow for Cu -water nanoliquids within a ciliated symmetric micro-channel, the flow is established with aid of ciliary motion and axial pressure gradient. Nanofluid comprise of Cu as a nanofluid particles and water as base fluid. Maxwell-Garnelt model is exploited for viscosity and thermal conductivity of nanoliquid. Magnetic field is applied in the transverse direction and external electric field is enforced in the axial direction. Equations of motion are simplified for nanofluid flow in the micro channel by employing low Reynolds number and long wavelength approximation theory. Crucial exact analytical expression are gathered for electric potential, temperature profile, axial velocity, volume flux, pressure gradient, stream function, and result for pressure rise per wavelength explored numerically. The influence of crucial flow parameters on, flow behaviour, pumping phenomena, and temperature profile are thoroughly investigated.Article Citation - WoS: 1Citation - Scopus: 1A Novel Fractional Model for the Projection of Households Using Wealth Index Quintiles(Public Library Science, 2022) Javeed, Shumaila; Raza, Saqlain; Baleanu, Dumitru; Ahmad, ShakoorForecasting household assets provides a better opportunity to plan their socioeconomic activities for the future. Fractional mathematical models offer to model the asset-holding data into a piece of scientific evidence in addition to forecasting their future value. This research focuses on the development of a new fractional mathematical model based on the wealth index quintile (WIQ) data. To accomplish the objective, we used the system of coupled fractional differential equations by defining the fractional term with the Caputo derivative and verified it with the stability tests considering the steady-state solution. A numerical solution of the model was obtained using the Adams-Bashforth-Moulton method. To validate the model, we used real-time data obtained from the household series of surveys in Punjab, Pakistan. Different case studies that elucidate the effect of quintiles on the population are also presented. The accuracy of results between real-world and simulated data was compared using absolute and relative errors. The synchronization between the simulated results and real-time data verifies the formulation of the fractional WIQ model. This fractional model can be utilized to predict the approximation of the asset-holding of the households. Due to its relative nature, the model also provides the opportunity for the researchers to use the WIQs of their respective regions to forecast the households' socioeconomic conditions.Article Solitons of the (1 + 1) - and (2 + 1) -Dimensional Chiral Nonlinear Schrodinger Equations with the Jacobi Elliptical Function Method(2023) Tala-Tebue, Eric; Rezazadeh, Hadi; Javeed, Shumaila; Baleanu, Dumitru; Korkmaz, AlperOur objective is to find new analytical solutions of the (1 + 1) - and (2 + 1) -dimensional Chiral nonlinear Schrodinger (CNLS) equations using the Jacobi elliptical function method. The CNLS equations play a significant role in the development of quantum mechanics, particularly in the field of quantum Hall effect. Soliton solutions of the considered models are obtained such as, cnoidal solutions, the hyperbolic solutions and the trigonometric solutions. The obtained analytical solutions are new in the literature. The stability conditions of these solutions are also given. The obtained stable solutions are presented graphically for some specific parameters. Moreover, the conditions of modulational instability for both models are provided. The proposed method can be useful to obtain the analytical solutions of nonlinear partial differential equations.Article Citation - WoS: 20Citation - Scopus: 19Numerical Solutions of the Wolbachia Invasive Model Using Levenberg-Marquardt Backpropagation Neural Network Technique(Elsevier, 2023) Javeed, Shumaila; Ahmed, Iftikhar; Baleanu, Dumitru; Riaz, Muhammad Bilal; Sabir, Zulqurnain; Faiz, Zeshan; Bilal Riaz, MuhammadThe current study presents the numerical solutions of the Wolbachia invasive model (WIM) using the neural network Levenberg-Marquardt (NN-LM) backpropagation technique. The dynamics of the Wolbachia model is categorized into four classes, namely Wolbachia-uninfected aquatic mosquitoes (A*n), Wolbachia-uninfected adult female mosquitoes (Fn*), Wolbachia-infected aquatic mosquitoes (A*w), and Wolbachia-infected adult female mosquitoes (F*w). A reference dataset for the proposed NN-LM technique is created by solving the Wolbachia model using the Runge-Kutta (RK) numerical method. The reference dataset is used for validation, training, and testing of the proposed NN-LM technique for three different cases. The obtained numerical results from the proposed neural network technique are compared with the results obtained from the RK method for accuracy, correctness, and efficiency of the designed methodology. The validation of the proposed solution methodology is checked through the mean square error (MSE), error histograms, error plots, regression plots, and fitness plots.Article Citation - WoS: 1Citation - Scopus: 4Fractional Modeling of Cancer With Mixed Therapies(Imr Press, 2023) Ul Abdeen, Zain; Baleanu, Dumitru; Javeed, ShumailaBackground: Cancer is the biggest cause of mortality globally, with approximately 10 million fatalities expected by 2020, or about one in every six deaths. Breast, lung, colon, rectum, and prostate cancers are the most prevalent types of cancer. Methods: In this work, fractional modeling is presented which describes the dynamics of cancer treatment with mixed therapies (immunotherapy and chemotherapy). Mathematical models of cancer treatment are important to understand the dynamical behavior of the disease. Fractional models are studied considering immunotherapy and chemotherapy to control cancer growth at the level of cell populations. The models consist of the system of fractional differential equations (FDEs). Fractional term is defined by Caputo fractional derivative. The models are solved numerically by using Adams-Bashforth-Moulton method. Results: For all fractional models the reasonable range of fractional order is between beta = 0.6 and beta = 0.9. The equilibrium points and stability analysis are presented. Moreover, positivity and boundedness of the solution are proved. Furthermore, a graphical representation of cancerous cells, immunotherapy and chemotherapy is presented to understand the behaviour of cancer treatment. Conclusions: At the end, a curve fitting procedure is presented which may help medical practitioners to treat cancer patients.Article Citation - WoS: 12Citation - Scopus: 16Soliton Solutions of Nonlinear Boussinesq Models Using the Exponential Function Technique(Iop Publishing Ltd, 2021) Baleanu, Dumitru; Nawaz, Sidra; Rezazadeh, Hadi; Javeed, ShumailaThis paper deals with the new analytical solutions of conformable nonlinear Boussinesq equations. Boussinesq equation is one of the important equation in the field of applied mathematics and engineering, particularly in optical fibers, plasma physics, fluid dynamics, signal processing, and shallow water etc. The focus of this paper is to obtain the new explicit solutions of conformable Boussinesq equations. Exponential function technique is employed to solve the considered models. The conformable properties are utilized to obtain new analytical solutions for this type of nonlinear Boussinesq equations. The new analytical solutions are acquired especially for the space-time boussinesq equation. The results are shown graphically. The obtained solutions can be useful for engineers and physicists to further analyze the phenomena. The implemented technique is valuable for finding new analytical solutions of nonlinear partial differential equations (PDEs).