Mohammed Althubyani^1,*, Nidal E. Taha², Khdija O. Taha², Rasmiyah A. Alharb², Sayed Saber^1,3

CMES-Computer Modeling in Engineering & Sciences, Vol.143, No.3, pp. 3491-3521, 2025, DOI:10.32604/cmes.2025.061640 - 30 June 2025

Abstract This study investigates the dynamics of pneumococcal pneumonia using a novel fractal-fractional Susceptible-Carrier-Infected-Recovered model formulated with the Atangana-Baleanu in Caputo (ABC) sense. Unlike traditional epidemiological models that rely on classical or Caputo fractional derivatives, the proposed model incorporates nonlocal memory effects, hereditary properties, and complex transmission dynamics through fractal-fractional calculus. The Atangana-Baleanu operator, with its non-singular Mittag-Leffler kernel, ensures a more realistic representation of disease progression compared to classical integer-order models and singular kernel-based fractional models. The study establishes the existence and uniqueness of the proposed system and conducts a comprehensive stability analysis, including local More >

Nadeem Ahmad Sheikh^1,2, Dennis Ling Chuan Ching¹, Thabet Abdeljawad^3,4,5, Ilyas Khan^6,*, Muhammad Jamil^7,8, Kottakkaran Sooppy Nisar⁹

CMC-Computers, Materials & Continua, Vol.67, No.2, pp. 1385-1398, 2021, DOI:10.32604/cmc.2021.011986 - 05 February 2021

Abstract An emerging definition of the fractal-fractional operator has been used in this study for the modeling of Casson fluid flow. The magnetohydrodynamics flow of Casson fluid has cogent in a channel where the motion of the upper plate generates the flow while the lower plate is at a static position. The proposed model is non-dimensionalized using the Pi-Buckingham theorem to reduce the complexity in solving the model and computation time. The non-dimensional fractal-fractional model with the power-law kernel has been solved through the Laplace transform technique. The Mathcad software has been used for illustration of… More >

Dolat Khan¹, Gohar Ali¹, Arshad Khan², Ilyas Khan^{3, *}, Yu-Ming Chu^{4, 5}, Kottakkaran Sooppy Nisar⁶

CMC-Computers, Materials & Continua, Vol.65, No.2, pp. 1237-1251, 2020, DOI:10.32604/cmc.2020.011492 - 20 August 2020

Abstract Nowadays some new ideas of fractional derivatives have been used successfully in the present research community to study different types of mathematical models. Amongst them, the significant models of fluids and heat or mass transfer are on priority. Most recently a new idea of fractal-fractional derivative is introduced; however, it is not used for heat transfer in channel flow. In this article, we have studied this new idea of fractal fractional operators with power-law kernel for heat transfer in a fluid flow problem. More exactly, we have considered the free convection heat transfer for a… More >