Manal. M. Alqarni¹, Arooj Nasir^2,3, Dumitru Baleanu^4,5,6, Ali Raza⁷, Tahir Nawaz Cheema^8,*, Nauman Ahmed⁹, Muhammad Rafiq¹⁰, Umbreen Fatima¹¹, Emad E. Mahmoud¹²

CMC-Computers, Materials & Continua, Vol.74, No.3, pp. 6807-6822, 2023, DOI:10.32604/cmc.2023.033283

Abstract Artificial intelligence is demonstrated by machines, unlike the natural intelligence displayed by animals, including humans. Artificial intelligence research has been defined as the field of study of intelligent agents, which refers to any system that perceives its environment and takes actions that maximize its chance of achieving its goals. The techniques of intelligent computing solve many applications of mathematical modeling. The research work was designed via a particular method of artificial neural networks to solve the mathematical model of coronavirus. The representation of the mathematical model is made via systems of nonlinear ordinary differential equations. These differential equations are established… More >

Zafar Iqbal^1,2, Muhammad Aziz-ur Rehman¹, Nauman Ahmed^1,2, Ali Raza^3,4, Muhammad Rafiq⁵, Ilyas Khan^6,*, Kottakkaran Sooppy Nisar⁷

CMC-Computers, Materials & Continua, Vol.71, No.2, pp. 2141-2157, 2022, DOI:10.32604/cmc.2022.013906

Abstract In this article, a brief biological structure and some basic properties of COVID-19 are described. A classical integer order model is modified and converted into a fractional order model with as order of the fractional derivative. Moreover, a valued structure preserving the numerical design, coined as Grunwald–Letnikov non-standard finite difference scheme, is developed for the fractional COVID-19 model. Taking into account the importance of the positivity and boundedness of the state variables, some productive results have been proved to ensure these essential features. Stability of the model at a corona free and a corona existing equilibrium points is investigated on… More >

Wasfi Shatanawi^1,2,3, Ali Raza^4,5,*, Muhammad Shoaib Arif⁴, Kamaledin Abodayeh¹, Muhammad Rafiq⁶, Mairaj Bibi⁷

CMC-Computers, Materials & Continua, Vol.66, No.2, pp. 1121-1137, 2021, DOI:10.32604/cmc.2020.012070

Abstract Nonlinear stochastic modeling plays a significant role in disciplines such as psychology, finance, physical sciences, engineering, econometrics, and biological sciences. Dynamical consistency, positivity, and boundedness are fundamental properties of stochastic modeling. A stochastic coronavirus model is studied with techniques of transition probabilities and parametric perturbation. Well-known explicit methods such as Euler Maruyama, stochastic Euler, and stochastic Runge–Kutta are investigated for the stochastic model. Regrettably, the above essential properties are not restored by existing methods. Hence, there is a need to construct essential properties preserving the computational method. The non-standard approach of finite difference is examined to maintain the above basic… More >