Yaqing Liu^a,*, Jinyu Ma^b

Frontiers in Heat and Mass Transfer, Vol.6, pp. 1-5, 2015, DOI:10.5098/hmt.6.17

Abstract This paper presents an exact solution for the magnetohydrodynamic (MHD) flow of an incompressible generalized Oldroyd-B fluid due to an infinite accelerating plate. The fractional calculus approach is introduced to establish the constitutive relationship of the Oldroyd-B fluid. The solutions in terms of Fox H-function are obtained by using the Laplace transform. When N = 0 the solutions corresponds to the generalized Oldroyd-B fluids, while θ → 0 and λ → 0 describes the Maxwell fluid and the generalized second fluid, as limiting cases of our general results, respectively. 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

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 and then determining the series… 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

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 transform merged with the mechanism… More >

Muhammad Ramzan^a,*, Zaib Un Nisa^b , Mudassar Nazar^a,c,†

Frontiers in Heat and Mass Transfer, Vol.19, pp. 1-9, 2022, DOI:10.5098/hmt.19.12

Abstract A magnetohydrodynamics (MHD) flow of fractional Maxwell fluid past an exponentially accelerated vertical plate is considered. In addition, other factors such as heat generation and chemical reaction are used in the problem. The flow model is solved using Caputo fractional derivative. Initially, the governing equations are made non-dimensional and then solved by Laplace transform. The influence of different parameters like diffusion thermo, fractional parameter, Magnetic field, chemical reaction, Prandtl number and Maxwell parameter are discussed through numerous graphs. From figures, it is observed that fluid motion decreases with increasing values of Schmidt number and chemical reaction, whereas velocity field decreases… 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

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 is fully suitable and time-efficient… 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

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 the existing solution. The proof… 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

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 ARIMA (1, 1, 2), and… 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

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 of integer order are in… 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

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 >