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Mohamed M. Khader, Ali H. Tedjani. NUMERICAL SIMULATION FOR THE FRACTIONAL-ORDER SMOKING MODEL USING A SPECTRAL COLLOCATION METHOD BASED ON THE GEGENBAUER WAVELET POLYNOMIALS[J]. Journal of Applied Analysis & Computation, 2024, 14(2): 847-863. doi: 10.11948/20230178
Citation: Mohamed M. Khader, Ali H. Tedjani. NUMERICAL SIMULATION FOR THE FRACTIONAL-ORDER SMOKING MODEL USING A SPECTRAL COLLOCATION METHOD BASED ON THE GEGENBAUER WAVELET POLYNOMIALS[J]. Journal of Applied Analysis & Computation, 2024, 14(2): 847-863. doi: 10.11948/20230178
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NUMERICAL SIMULATION FOR THE FRACTIONAL-ORDER SMOKING MODEL USING A SPECTRAL COLLOCATION METHOD BASED ON THE GEGENBAUER WAVELET POLYNOMIALS

  • 1.

    Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11566, Saudi Arabia

  • 2.

    Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt

    Abstract

  • Smoking is a social trend that is prevalent around the world, particularly in places of learning and at some significant events. The World Health Organization (WHO) defines smoking as the most important preventable cause of disease and the third major cause of death in humans. So, in this paper, we present an effective simulation to study the solution behavior of the Liouville-Caputo fractional-order smoking model by using a presumably new approximation technique that is based on the Gegenbauer wavelet polynomials (GWPs). We use the spectral collocation method based on the properties of GWPs. This procedure converts the given model into a system of algebraic equations. We satisfy the efficiency and accuracy of the given procedure by evaluating the residual error function. The results obtained are then compared with the results obtained by using the fourth-order Runge-Kutta method. Our results show that the implemented technique provides an easy and efficient tool to simulate the solution of such smoking models.

    MSC: 34A12, 41A30, 47H10, 65N20
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