Browsing by Author "Karim, Shazia"

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Citation - WoS: 3
Citation - Scopus: 3
Identification of numerical solutions of a fractal-fractional divorce epidemic model of nonlinear systems via anti-divorce counseling
(Amer inst Mathematical Sciences-aims, 2023) Al-Qurashi, Maysaa; Jarad, Fahd; Sultana, Sobia; Karim, Shazia; Rashid, Saima; Jarad, Fahd; Alharthi, Mohammed Shaaf; 234808; Matematik
Divorce is the dissolution of two parties' marriage. Separation and divorce are the major obstacles to the viability of a stable family dynamic. In this research, we employ a basic incidence functional as the source of interpersonal disagreement to build an epidemiological framework of divorce outbreaks via the fractal-fractional technique in the Atangana-Baleanu perspective. The research utilized Lyapunov processes to determine whether the two steady states (divorce-free and endemic steady state point) are globally asymptotically robust. Local stability and eigenvalues methodologies were used to examine local stability. The next-generation matrix approach also provides the fundamental reproducing quantity over bar R0. The existence and stability of the equilibrium point can be assessed using R over bar 0, demonstrating that counseling services for the separated are beneficial to the individuals' well-being and, as a result, the population. The fractal-fractional Atangana-Baleanu operator is applied to the divorce epidemic model, and an innovative technique is used to illustrate its mathematical interpretation. We compare the fractal-fractional model to a framework accommodating different fractal-dimensions and fractional-orders and deduce that the fractal-fractional data fits the stabilized marriages significantly and cannot break again.
Citation - WoS: 9
Citation - Scopus: 11
Optimal variational iteration method for parametric boundary value problem
(Amer inst Mathematical Sciences-aims, 2022) Ain, Qura Tul; Jarad, Fahd; Nadeem, Muhammad; Karim, Shazia; Akguel, Ali; Jarad, Fahd; 234808; Matematik
Mathematical applications in engineering have a long history. One of the most well-known analytical techniques, the optimal variational iteration method (OVIM), is utilized to construct a quick and accurate algorithm for a special fourth-order ordinary initial value problem. Many researchers have discussed the problem involving a parameter c. We solve the parametric boundary value problem that can't be addressed using conventional analytical methods for greater values of c using a new method and a convergence control parameter h. We achieve a convergent solution no matter how huge c is. For the approximation of the convergence control parameter h, two strategies have been discussed. The advantages of one technique over another have been demonstrated. Optimal variational iteration method can be seen as an effective technique to solve parametric boundary value problem.