Model of Thin Viscous Fluid Sheet Flow within the Scope of Fractional Calculus: Fractional Derivative with and No Singular Kernel

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: Atangana, Abdon^{a; *} | Koca, Ilknur^b

Affiliations: [a] Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, 9300, Bloemfontein, South Africa. abdonatangana@yahoo.fr | [b] Department of Mathematics, Faculty of Sciences, Mehmet Akif Ersoy University, 15100, Burdur, Turkey

Correspondence: [*] Address for correspondence: Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, 9300, Bloemfontein, South Africa

Abstract: A comparative analysis of a model of thin viscous fluid sheet flow between Caputo and Caputo-Fabrizio derivative with fractional order was performed in this work. Sides-by-sides we presented some properties of both derivatives, and then we examined the existence of the exact solution of both nonlinear equations via the fixed-point theorem. A detailed study of the uniqueness of analysis for both models is presented. Numerical simulations are presented to access the difference between both models.

Keywords: Caputo derivative, Caputo-Fabrizio derivative, thin viscous fluid sheet flow model, existence and uniqueness of exact solution

DOI: 10.3233/FI-2017-1484

Journal: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 145-159, 2017