Thabet Abdeljawad^1,2, Awais Younus^3,*, Manar A. Alqudah⁴, Usama Atta⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.134, No.3, pp. 2163-2191, 2023, DOI:10.32604/cmes.2022.020915 - 20 September 2022

Abstract The Laplace transformation is a very important integral transform, and it is extensively used in solving ordinary differential equations, partial differential equations, and several types of integro-differential equations. Our purpose in this study is to introduce the notion of fuzzy double Laplace transform, fuzzy conformable double Laplace transform (FCDLT). We discuss some basic properties of FCDLT. We obtain the solutions of fuzzy partial differential equations (both one-dimensional and two-dimensional cases) through the double Laplace approach. We demonstrate through numerical examples that our proposed method is very successful and convenient for resolving partial differential equations. More >

Kamal Shah^1,2, Hafsa Naz², Thabet Abdeljawad^1,3,*, Aziz Khan¹, Manar A. Alqudah⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.134, No.2, pp. 941-955, 2023, DOI:10.32604/cmes.2022.021483 - 31 August 2022

Abstract In this manuscript, an algorithm for the computation of numerical solutions to some variable order fractional differential equations (FDEs) subject to the boundary and initial conditions is developed. We use shifted Legendre polynomials for the required numerical algorithm to develop some operational matrices. Further, operational matrices are constructed using variable order differentiation and integration. We are finding the operational matrices of variable order differentiation and integration by omitting the discretization of data. With the help of aforesaid matrices, considered FDEs are converted to algebraic equations of Sylvester type. Finally, the algebraic equations we get are 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 >

Ying Li¹, Longxiang Xu¹, Fangjun Mei¹, Shihui Ying^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.134, No.1, pp. 657-672, 2023, DOI:10.32604/cmes.2022.021277 - 24 August 2022

Abstract We propose new hybrid Lagrange neural networks called LaNets to predict the numerical solutions of partial differential equations. That is, we embed Lagrange interpolation and small sample learning into deep neural network frameworks. Concretely, we first perform Lagrange interpolation in front of the deep feedforward neural network. The Lagrange basis function has a neat structure and a strong expression ability, which is suitable to be a preprocessing tool for pre-fitting and feature extraction. Second, we introduce small sample learning into training, which is beneficial to guide the model to be corrected quickly. Taking advantages of More >

Augusto González Bonorino^1,*, Malick Ndiaye², Casimer DeCusatis²

Journal of Quantum Computing, Vol.4, No.3, pp. 135-146, 2022, DOI:10.32604/jqc.2022.036706 - 03 July 2023

Abstract The well-known Riccati differential equations play a key role in many fields, including problems in protein folding, control and stabilization, stochastic control, and cybersecurity (risk analysis and malware propagation). Quantum computer algorithms have the potential to implement faster approximate solutions to the Riccati equations compared with strictly classical algorithms. While systems with many qubits are still under development, there is significant interest in developing algorithms for near-term quantum computers to determine their accuracy and limitations. In this paper, we propose a hybrid quantum-classical algorithm, the Matrix Riccati Solver (MRS). This approach uses a transformation of More >

Mustafa Turkyilmazoglu^1,2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.133, No.1, pp. 47-65, 2022, DOI:10.32604/cmes.2022.020781 - 18 July 2022

Abstract An effective solution method of fractional ordinary and partial differential equations is proposed in the present paper. The standard Adomian Decomposition Method (ADM) is modified via introducing a functional term involving both a variable and a parameter. A residual approach is then adopted to identify the optimal value of the embedded parameter within the frame of L² norm. Numerical experiments on sample problems of open literature prove that the presented algorithm is quite accurate, more advantageous over the traditional ADM and straightforward to implement for the fractional ordinary and partial differential equations of the recent focus More >

Nezihal Gokbulut^1,2, Evren Hincal^1,2,*, Hasan Besim³, Bilgen Kaymakamzade^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.133, No.1, pp. 93-109, 2022, DOI:10.32604/cmes.2022.019782 - 18 July 2022

Abstract Breast Imaging Reporting and Data System, also known as BI-RADS is a universal system used by radiologists and doctors. It constructs a comprehensive language for the diagnosis of breast cancer. BI-RADS 4 category has a wide range of cancer risk since it is divided into 3 categories. Mathematical models play an important role in the diagnosis and treatment of cancer. In this study, data of 42 BI-RADS 4 patients taken from the Center for Breast Health, Near East University Hospital is utilized. Regarding the analysis, a mathematical model is constructed by dividing the population into… More >

A. B. Vishalakshi¹, U. S. Mahabaleshwar^1,*, M. EL. Ganaoui², R. Bennacer³

FDMP-Fluid Dynamics & Materials Processing, Vol.18, No.5, pp. 1551-1567, 2022, DOI:10.32604/fdmp.2022.021949 - 27 May 2022

Abstract This paper is devoted to the analysis of the heat transfer and Navier’s slip effects in a non-Newtonian Jeffrey fluid flowing past a stretching/shrinking sheet. The nanoparticles, namely, Cu and Al₂O₃ are used with a water-based fluid with Prandtl number 6.272. Velocity slip flow is assumed to occur when the characteristic size of the flow system is small or the flow pressure is very small. By using the similarity transformations, the governing nonlinear PDEs are turned into ordinary differential equations (ODE’s). Analytical results are presented and analyzed for various values of physical parameters: Prandtl number, Radiation… More >

Hira Soomro^1,*, Nooraini Zainuddin¹, Hanita Daud¹, Joshua Sunday²

CMC-Computers, Materials & Continua, Vol.72, No.2, pp. 2947-2961, 2022, DOI:10.32604/cmc.2022.025933 - 29 March 2022

Abstract Multistep integration methods are being extensively used in the simulations of high dimensional systems due to their lower computational cost. The block methods were developed with the intent of obtaining numerical results on numerous points at a time and improving computational efficiency. Hybrid block methods for instance are specifically used in numerical integration of initial value problems. In this paper, an optimized hybrid block Adams block method is designed for the solutions of linear and nonlinear first-order initial value problems in ordinary differential equations (ODEs). In deriving the method, the Lagrange interpolation polynomial was employed… More >

Rohul Amin¹, Şuayip Yüzbası^2,*, Shah Nazir³

CMES-Computer Modeling in Engineering & Sciences, Vol.131, No.2, pp. 639-653, 2022, DOI:10.32604/cmes.2022.019154 - 14 March 2022

Abstract In this paper, Haar collocation algorithm is developed for the solution of first-order of HIV infection CD4⁺ T-Cells model. In this technique, the derivative in the nonlinear model is approximated by utilizing Haar functions. The value of the unknown function is obtained by the process of integration. Error estimation is also discussed, which aims to reduce the error of numerical solutions. The numerical results show that the method is simply applicable. The results are compared with Runge-Kutta technique, Bessel collocation technique, LADM-Pade and Galerkin technique available in the literature. The results show that the Haar technique More >