On Non-Parametric Criteria for Random Communication and Processes Relationship

Farah, Abdulkarim; Dababneh, Amer; Zraiqat, Amjed

doi:10.29294/ijase.7.2.2020.1675-1690

Cited by 3 publications

(2 citation statements)

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“…Based on these simulations it can be determined that the fractionalorder version of the differential system of the ICT carried out by the two numerical methods (FEM and MFEM) are completely considered. For more about fractional calculus and its applications, the reader may refer to [6,8,10,13,14].…”

Section: Numerical Resultsmentioning

confidence: 99%

Numerical Solution for Fractional-Order Mathematical Model of Immune-Chemotherapeutic Treatment for Breast Cancer Using Modified Fractional Formula

Abu Hammad,

Jebril,

Alshorm

et al. 2023

Int. J. Anal. Appl.

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Cancer is a complex and diverse group of diseases characterized by the uncontrolled growth and spread of abnormal cells in the body. Tumors, which are commonly associated with cancer, refer to abnormal masses of tissue that can develop in various organs or tissues. Cancer can arise from almost any cell type in the body and can affect different organs and systems. The disease occurs when the normal processes of cell division and growth go awry, leading to the formation of malignant tumors. These tumors have the potential to invade nearby tissues and spread to distant parts of the body through a process known as metastasis. In this paper, we aim to present a numerical solution for a recent fractional-order model related to Immune-Chemotherapeutic Treatment for Breast Cancer (ICT) using a novel numerical scheme called the Modified Fractional Euler Method (MFEM). We will also compare our proposed scheme with the traditional numerical scheme, Fractional Euler Method (FEM), through numerical simulations.

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Section: Numerical Resultsmentioning

confidence: 99%

Numerical Solution for Fractional-Order Mathematical Model of Immune-Chemotherapeutic Treatment for Breast Cancer Using Modified Fractional Formula

Abu Hammad,

Jebril,

Alshorm

et al. 2023

Int. J. Anal. Appl.

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“…In Section 3, we scrutinize a bilinear model with exponential coefficients, assessing the hypotheses of the Klimko-Nilsen theorem and detailing the approach to estimating model coefficients. In Section 4, with applications and numerical illustrations, including MATLAB-generated graphs, our study concludes with general remarks and comments on the broader implications of our research in the realm of time series analysis involving bilinear models with time-varying exponential coefficients [5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Novel Insights into Estimation of Bilinear Time Series Models with Exponential and Symmetric Coefficients

Abu Hammad,

Laiche,

Alomari

et al. 2024

Symmetry

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This paper focuses on the estimation and simulation of a specific subset of bilinear time series models characterized by dynamic exponential coefficients. Employing an exponential framework, we delve into the implications of the exponential function for our estimation process. Our primary aim is to estimate the coefficients of the proposed model using exponential coefficients derived from time-varying parameters. Through this investigation, our goal is to shed light on the asymptotic behaviors of the estimators and scrutinize their existence and probabilistic traits, drawing upon the foundational theorem established by Klimko and Nilsen. The least squares approach is pivotal in both estimating coefficients and analyzing estimator behavior. Moreover, we present a practical application to underscore the real-world implications of our research. By offering concrete examples of applications and simulations, we endeavor to provide readers with a comprehensive understanding of the implications of our work within the realm of time series analysis, specifically focusing on bilinear models and time-varying exponential coefficients. This multifaceted approach underscores the potential impact and practical relevance of our findings, contributing to the advancement of the field of time series analysis. To discern the symmetry characteristics of the model, we estimate it using coefficients that sum to zero and conduct a brief comparative analysis of two bilinear models.

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