Analysis of Riccati Differential Equations within a New Fractional Derivative without 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: Jafari, Hossein^{a; *} | Lia, Atena^a | Tejadodi, Haleh^{b; *} | Baleanu, Dumitru^{c; d}

Affiliations: [a] Department of Mathematics, University of Mazandaran, P.O.Box 47416-95447, Babolsar, Iran. jafari@umz.ac.ir | [b] Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran | [c] Department of Mathematics, Cankaya University, 06530 Ankara, Turkey | [d] Institute of Space Sciences, P.O. BOX, MG-23, 76900 Magurele-Bucharest, Romania

Correspondence: [*] Address for correspondence: Department of Mathematics, University of Mazandaran, P.O.Box 47416-95447, Babolsar, Iran

Note: [*] Also affiliated at: Department of Mathematical Sciences, University of South Africa, P.O. Box 392, UNISA 0003, South Africa

Abstract: Recently Caputo and Fabrizio suggested new definition of fractional derivative that the new kernel has no singularity. In this paper, an analytical method for solving Riccati differential equation with a new fractional derivative is reported. We present numerical results of solving the fractional Riccati differential equations by using the variational iteration method and its modification. The obtained results of two methods demonstrate the efficiency and simplicity of the MVIM that gives good approximations for a larger interval.

Keywords: Caputo-Fabrizio derivative, Riccati differential equations, Fractional derivative

DOI: 10.3233/FI-2017-1485

Journal: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 161-171, 2017