A New Approach for Modeling with Discrete Fractional Equations

Issue title: Theory and Applications of Fractional Fourier Transform and its Variants

Guest editors: Yudong Zhang, Xiao-Jun Yang, Carlo Cattani, Zhengchao Dong, Ti-Fei Yuan and Liang-Xiu Han

Article type: Research Article

Authors: Atıcı, Ferhan M.^{a; *} | Atıcı, Mustafa^b | Belcher, Michael^c | Marshall, Dana^d

Affiliations: [a] Department of Mathematics, Western Kentucky University, Bowling Green, Kentucky 42101-3576 USA. ferhan.atici@wku.edu | [b] Department of Computer Science, Western Kentucky University, Bowling Green, Kentucky 42101-3576 USA. mustafa.atici@wku.edu | [c] Gatton Academy of Science and Mathematics, Bowling Green, Kentucky 42101 USA. michael.belcher403@topper.wku.edu | [d] Department of Pathology, Anatomy and Cell Biology, Meharry Medical College, Nashville, Tennessee 37208 USA. dmarshall@mmc.edu

Correspondence: [*] Address for correspondence: Department of Mathematics, Western Kentucky University, Bowling Green, Kentucky 42101-3576 USA

Abstract: In this paper, we introduce a new class of nonlinear discrete fractional equations to model tumor growth rates in mice. For the data fitting purpose, we develop a new method which can be considered as an improved version of the partial sum method for parameter estimations. We demonstrate the goodness of fit by comparing the models with three statistical measures.

Keywords: Discrete Fractional Calculus, Parameter Estimations, Data Fitting, Method of Partial Sums

DOI: 10.3233/FI-2017-1494

Journal: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 313-324, 2017