Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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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 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).Article Citation - WoS: 4Citation - Scopus: 5Ginzburg Landau Equation's Innovative Solution (Gleis)(Iop Publishing Ltd, 2021) Rezazadeh, Hadi; Baleanu, Dumitru; Desta Leta, Temesgen; Javeed, Shumaila; Alimgeer, Khurram Saleem; El Achab, Abdelfattah; Achab, Abdelfattah E.L.; Leta, Temesgen DestaA novel soliton solution of the famous 2D Ginzburg-Landau equation is obtained. A powerful Sine-Gordon expansion method is used for acquiring soliton solutions 2D Ginzburg-Landau equation. These solutions are obtained with the help of contemporary software (Maple) that allows computation of equations within the symbolic format. Some new solutions are depicted in the forms of figures. The Sine-Gordon method is applicable for solving various non-linear complex models such as, Quantum mechanics, plasma physics and biological science.Article Citation - WoS: 18Citation - Scopus: 23First Integral Technique for Finding Exact Solutions of Higher Dimensional Mathematical Physics Models(Mdpi, 2019) Riaz, Sidra; Alimgeer, Khurram Saleem; Atif, M.; Hanif, Atif; Baleanu, Dumitru; Javeed, ShumailaIn this work, we establish the exact solutions of some mathematical physics models. The first integral method (FIM) is extended to find the explicit exact solutions of high-dimensional nonlinear partial differential equations (PDEs). The considered models are: the space-time modified regularized long wave (mRLW) equation, the (1+2) dimensional space-time potential Kadomtsev Petviashvili (pKP) equation and the (1+2) dimensional space-time coupled dispersive long wave (DLW) system. FIM is a powerful mathematical tool that can be used to obtain the exact solutions of many non-linear PDEs.