Maha Noorwali¹, Mohammed Shehu Shagari^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.137, No.2, pp. 1937-1956, 2023, DOI:10.32604/cmes.2023.028239

Abstract The real world is filled with uncertainty, vagueness, and imprecision. The concepts we meet in everyday life are vague rather than precise. In real-world situations, if a model requires that conclusions drawn from it have some bearings on reality, then two major problems immediately arise, viz. real situations are not usually crisp and deterministic; complete descriptions of real systems often require more comprehensive data than human beings could recognize simultaneously, process and understand. Conventional mathematical tools which require all inferences to be exact, are not always efficient to handle imprecisions in a wide variety of practical situations. Following the latter… More >

Ouafaa Bouftouh¹, Samir Kabbaj¹, Thabet Abdeljawad^2,3,*, Aziz Khan²

CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.3, pp. 2649-2663, 2023, DOI:10.32604/cmes.2023.023496

Abstract Generally, the field of fixed point theory has attracted the attention of researchers in different fields of science and engineering due to its use in proving the existence and uniqueness of solutions of real-world dynamic models. C^*-algebra is being continually used to explain a physical system in quantum field theory and statistical mechanics and has subsequently become an important area of research. The concept of a C^*-algebra-valued metric space was introduced in 2014 to generalize the concept of metric space. In fact, It is a generalization by replacing the set of real numbers with a C^*-algebra. After that, this line… More >

Nawab Hussain^1,*, Saud M. Alsulami¹, Hind Alamri^1,2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.3, pp. 2617-2648, 2023, DOI:10.32604/cmes.2023.023143

Abstract In this paper, we present the existence and uniqueness of fixed points and common fixed points for Reich and Chatterjea pairs of self-maps in complete metric spaces. Furthermore, we study fixed point theorems for Reich and Chatterjea nonexpansive mappings in a Banach space using the Krasnoselskii-Ishikawa iteration method associated with and consider some applications of our results to prove the existence of solutions for nonlinear integral and nonlinear fractional differential equations. We also establish certain interesting examples to illustrate the usability of our results. More >

Khursheed J. Ansari¹, Mustafa Inc^2,3,4,*, K. H. Mahmoud^5,*, Eiman⁶

CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.2, pp. 1669-1684, 2023, DOI:10.32604/cmes.2022.022971

Abstract In this article, we developed sufficient conditions for the existence and uniqueness of an approximate solution to a nonlinear system of Lorenz equations under Caputo-Fabrizio fractional order derivative (CFFD). The required results about the existence and uniqueness of a solution are derived via the fixed point approach due to Banach and Krassnoselskii. Also, we enriched our work by establishing a stable result based on the Ulam-Hyers (U-H) concept. Also, the approximate solution is computed by using a hybrid method due to the Laplace transform and the Adomian decomposition method. We computed a few terms of the required solution through the… More >

Naeem Saleem¹, Khalil Javed², Fahim Uddin³, Umar Ishtiaq⁴, Khalil Ahmed², Thabet Abdeljawad^5,6,*, Manar A. Alqudah⁷

CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.1, pp. 109-131, 2023, DOI:10.32604/cmes.2022.021031

Abstract In this manuscript, our goal is to introduce the notion of intuitionistic extended fuzzy b-metric-like spaces. We establish some fixed point theorems in this setting. Also, we plot some graphs of an example of obtained result for better understanding. We use the concepts of continuous triangular norms and continuous triangular conorms in an intuitionistic fuzzy metric-like space. Triangular norms are used to generalize with the probability distribution of triangle inequality in metric space conditions. Triangular conorms are known as dual operations of triangular norms. The obtained results boost the approaches of existing ones in the literature and are supported by… More >

Kastriot Zoto¹, Ilir Vardhami², Dušan Bajović³, Zoran D. Mitrović^3,*, Stojan Radenović⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.1, pp. 673-686, 2023, DOI:10.32604/cmes.2022.022878

Abstract The focus of our work is on the most recent results in fixed point theory related to contractive mappings. We describe variants of -contractions that expand, supplement and unify an important work widely discussed in the literature, based on existing classes of interpolative and -contractions. In particular, a large class of contractions in terms of and F for both linear and nonlinear contractions are defined in the framework of -metric-like spaces. The main result in our paper is that --weak contractions have a fixed point in -metric-like spaces if function F or the specified contraction is continuous. As an application… More >

M. J. Huntul^1,*, Taki-Eddine Oussaeif²

Computer Systems Science and Engineering, Vol.40, No.3, pp. 1109-1126, 2022, DOI:10.32604/csse.2022.020175

Abstract In this paper, we consider the unique solvability of the inverse problem of determining the right-hand side of a parabolic equation whose leading coefficient depends on time variable under nonlocal integral overdetermination condition. We obtain sufficient conditions for the unique solvability of the inverse problem. The existence and uniqueness of the solution of the inverse parabolic problem upon the data are established using the fixed point theorem. This inverse problem appears extensively in the modelling of various phenomena in engineering and physics. For example, seismology, medicine, fusion welding, continuous casting, metallurgy, aircraft, oil and gas production during drilling and operation… More >

Wasfi Shatanawi^{1, 2, 3, *}, Anwar Bataihah⁴, Abdalla Tallafha⁴

CMC-Computers, Materials & Continua, Vol.64, No.3, pp. 1491-1504, 2020, DOI:10.32604/cmc.2020.010365

Abstract Fixed point theory is one of the most important subjects in the setting of metric spaces since fixed point theorems can be used to determine the existence and the uniqueness of solutions of such mathematical problems. It is known that many problems in applied sciences and engineering can be formulated as functional equations. Such equations can be transferred to fixed point theorems in an easy manner. Moreover, we use the fixed point theory to prove the existence and uniqueness of solutions of such integral and differential equations. Let X be a non-empty set. A fixed point for a self-mapping T… More >

Abd-Allah Hyder^{1, 2, *}, M. El-Badawy³

CMC-Computers, Materials & Continua, Vol.64, No.2, pp. 859-870, 2020, DOI:10.32604/cmc.2020.09897

Abstract In this paper, the non-stationary incompressible fluid flows governed by the Navier-Stokes equations are studied in a bounded domain. This study focuses on the timefractional Navier-Stokes equations in the optimal control subject, where the control is distributed within the domain and the time-fractional derivative is proposed as RiemannLiouville sort. In addition, the control object is to minimize the quadratic cost functional. By using the Lax-Milgram lemma with the assistance of the fixed-point theorem, we demonstrate the existence and uniqueness of the weak solution to this system. Moreover, for a quadratic cost functional subject to the time-fractional Navier-Stokes equations, we prove… More >

Alfredo Nicolás¹, Blanca Bermúdez²

CMES-Computer Modeling in Engineering & Sciences, Vol.82, No.3&4, pp. 163-178, 2011, DOI:10.32604/cmes.2011.082.163

Abstract Mixed convection viscous incompressible fluid flows, under a gravitational system, in rectangular cavities are reported using the unsteady Boussinessq approximation in velocity-vorticity variables. The results are obtained using a numerical method based on a fixed point iterative process to solve the nonlinear elliptic system that results after time discretization; the iterative process leads to the solution of uncoupled, well-conditioned, symmetric linear elliptic problems for which efficient solvers exist regardless of the space discretization. Results with different aspect ratios A up to Grashof numbers Gr = 100000 and Reynolds numbers Re = 1000 for the lid driven cavity problem are reported.… More >