Daasara Keshavamurthy Archana¹, Doddabhadrappla Gowda Prakasha¹, Pundikala Veeresha², Kottakkaran Sooppy Nisar^3,4,*

CMES-Computer Modeling in Engineering & Sciences, Vol.141, No.2, pp. 1347-1363, 2024, DOI:10.32604/cmes.2024.053916 - 27 September 2024

Abstract This study intends to examine the analytical solutions to the resulting one-dimensional differential equation of a cancer tumor model in the frame of time-fractional order with the Caputo-fractional operator employing a highly efficient methodology called the -homotopy analysis transform method. So, the preferred approach effectively found the analytic series solution of the proposed model. The procured outcomes of the present framework demonstrated that this method is authentic for obtaining solutions to a time-fractional-order cancer model. The results achieved graphically specify that the concerned paradigm is dependent on arbitrary order and parameters and also disclose the More >

Nasser Sweilam¹, Seham Al-Mekhlafi^2,*, Aya Ahmed³, Ahoud Alsheri⁴, Emad Abo-Eldahab³

CMES-Computer Modeling in Engineering & Sciences, Vol.140, No.2, pp. 1619-1645, 2024, DOI:10.32604/cmes.2024.047896 - 20 May 2024

Abstract In this paper, two crossover hybrid variable-order derivatives of the cancer model are developed. Grünwald-Letnikov approximation is used to approximate the hybrid fractional and variable-order fractional operators. The existence, uniqueness, and stability of the proposed model are discussed. Adams Bashfourth’s fifth-step method with a hybrid variable-order fractional operator is developed to study the proposed models. Comparative studies with generalized fifth-order Runge-Kutta method are given. Numerical examples and comparative studies to verify the applicability of the used methods and to demonstrate the simplicity of these approximations are presented. We have showcased the efficiency of the proposed More >

Yu-Ming Chu¹, Sobia Sultana², Shazia Karim³, Saima Rashid^4,*, Mohammed Shaaf Alharthi⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.138, No.1, pp. 761-791, 2024, DOI:10.32604/cmes.2023.028600 - 22 September 2023

Abstract The goal of this research is to develop a new, simplified analytical method known as the ARA-residue power series method for obtaining exact-approximate solutions employing Caputo type fractional partial differential equations (PDEs) with variable coefficient. ARA-transform is a robust and highly flexible generalization that unifies several existing transforms. The key concept behind this method is to create approximate series outcomes by implementing the ARA-transform and Taylor’s expansion. The process of finding approximations for dynamical fractional-order PDEs is challenging, but the ARA-residual power series technique magnifies this challenge by articulating the solution in a series pattern… More >

Yu-Ming Chu¹, Saima Rashid^2,*, Shazia Karim³, Anam Sultan²

CMES-Computer Modeling in Engineering & Sciences, Vol.137, No.2, pp. 1573-1611, 2023, DOI:10.32604/cmes.2023.027724 - 26 June 2023

Abstract The fractional-order Boussinesq equations (FBSQe) are investigated in this work to see if they can effectively improve the situation where the shallow water equation cannot directly handle the dispersion wave. The fuzzy forms of analytical FBSQe solutions are first derived using the Adomian decomposition method. It also occurs on the sea floor as opposed to at the functionality. A set of dynamical partial differential equations (PDEs) in this article exemplify an unconfined aquifer flow implication. This methodology can accurately simulate climatological intrinsic waves, so the ripples are spread across a large demographic zone. The Aboodh… More >

Ahmad Shafique^a , Muhammad Ramzan^a,*, Zubda Ikram^a, M. Amir^a, Mudassar Nazar^a

Frontiers in Heat and Mass Transfer, Vol.20, pp. 1-10, 2023, DOI:10.5098/hmt.20.4

Abstract Unsteady flow of fractionalized Jeffrey fluid over a plate is considered. In addition, thermo diffusion and slip effects are also used in the problem. The flow model is solved using Constant proportional Caputo fractional derivative. Initially, the governing equations are made non-dimensional and then solved by Laplace transform. From the Figs., it is observed that Prandtl and Smith numbers have decreasing effect on fluid motion, whereas thermodiffusion have increasing effect on fluid motion. Moreover, comparison among fractionalized and ordinary velocity fields is also drawn. More >

Pushpendra Kumar^1,*, Vedat Suat Erturk², V. Govindaraj¹, Dumitru Baleanu^3,4,5

CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.3, pp. 2487-2506, 2023, DOI:10.32604/cmes.2023.026009 - 09 March 2023

Abstract In this article, we introduce a nonlinear Caputo-type snakebite envenoming model with memory. The well-known Caputo fractional derivative is used to generalize the previously presented integer-order model into a fractional-order sense. The numerical solution of the model is derived from a novel implementation of a finite-difference predictor-corrector (L1-PC) scheme with error estimation and stability analysis. The proof of the existence and positivity of the solution is given by using the fixed point theory. From the necessary simulations, we justify that the first-time implementation of the proposed method on an epidemic model shows that the scheme More >

Muath Awadalla^1,*, Kinda Abuasbeh¹, Yves Yannick Yameni Noupoue², Mohammed S. Abdo³

CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.3, pp. 2767-2785, 2023, DOI:10.32604/cmes.2023.024036 - 23 November 2022

Abstract This study focuses on the dynamics of drug concentration in the blood. In general, the concentration level of a drug in the blood is evaluated by the mean of an ordinary and first-order differential equation. More precisely, it is solved through an initial value problem. We proposed a new modeling technique for studying drug concentration in blood dynamics. This technique is based on two fractional derivatives, namely, Caputo and Caputo-Fabrizio derivatives. We first provided comprehensive and detailed proof of the existence of at least one solution to the problem; we later proved the uniqueness of… More >

Abeer S. Alnahdi^1,*, Mdi B. Jeelani¹, Hanan A. Wahash², Mansour A. Abdulwasaa^3,4

CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.2, pp. 1315-1343, 2023, DOI:10.32604/cmes.2022.023694 - 27 October 2022

Abstract This study aims to structure and evaluate a new COVID-19 model which predicts vaccination effect in the Kingdom of Saudi Arabia (KSA) under Atangana-Baleanu-Caputo (ABC) fractional derivatives. On the statistical aspect, we analyze the collected statistical data of fully vaccinated people from June 01, 2021, to February 15, 2022. Then we apply the Eviews program to find the best model for predicting the vaccination against this pandemic, based on daily series data from February 16, 2022, to April 15, 2022. The results of data analysis show that the appropriate model is autoregressive integrated moving average… More >

Dandan Dai¹, Xiaoyu Li², Zhiyuan Li², Wei Zhang³, Yulan Wang^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.2, pp. 1371-1392, 2023, DOI:10.32604/cmes.2022.022323 - 27 October 2022

Abstract Although some numerical methods of the fractional-order chaotic systems have been announced, high-precision numerical methods have always been the direction that researchers strive to pursue. Based on this problem, this paper introduces a high-precision numerical approach. Some complex dynamic behavior of fractional-order Lorenz chaotic systems are shown by using the present method. We observe some novel dynamic behavior in numerical experiments which are unlike any that have been previously discovered in numerical experiments or theoretical studies. We investigate the influence of , , on the numerical solution of fractional-order Lorenz chaotic systems. The simulation results More >

Ahmed M. Elshenhab^1,2,*, Xingtao Wang¹, Fatemah Mofarreh³, Omar Bazighifan^4,*

CMES-Computer Modeling in Engineering & Sciences, Vol.134, No.2, pp. 927-940, 2023, DOI:10.32604/cmes.2022.021512 - 31 August 2022

Abstract We study nonhomogeneous systems of linear conformable fractional differential equations with pure delay. By using new conformable delayed matrix functions and the method of variation, we obtain a representation of their solutions. As an application, we derive a finite time stability result using the representation of solutions and a norm estimation of the conformable delayed matrix functions. The obtained results are new, and they extend and improve some existing ones. Finally, an example is presented to illustrate the validity of our theoretical results. More >