On Analytical Solutions of the Fractional Differential Equation with Uncertainty: Application to the Basset Problem

Entropy

Soheil Salahshour²  Ali Ahmadian¹  Norazak Senu¹  Dumitru Baleanu³ 

[1] Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400UPM, Serdang, Selangor, Malaysia; E-Mails:;Young Researchers and Elite Club, Mobarakeh Branch, Islamic Azad University, Mobarakeh, Iran;Department of Mathematics and Computer Sciences, Faculty of Art and Sciences, Cankaya University, Balgat 0630, Ankara, Turkey; E-Mail:

关键词: fuzzy fractional differential equation;    fuzzy Laplace transform;    Caputo differentiability;    dynamical systems;    Basset problem;   

DOI  :  10.3390/e17020885

来源: mdpi

【 摘 要 】

In this paper, we apply the concept of Caputo’s H-differentiability, constructed based on the generalized Hukuhara difference, to solve the fuzzy fractional differential equation (FFDE) with uncertainty. This is in contrast to conventional solutions that either require a quantity of fractional derivatives of unknown solution at the initial point (Riemann–Liouville) or a solution with increasing length of their support (Hukuhara difference). Then, in order to solve the FFDE analytically, we introduce the fuzzy Laplace transform of the Caputo H-derivative. To the best of our knowledge, there is limited research devoted to the analytical methods to solve the FFDE under the fuzzy Caputo fractional differentiability. An analytical solution is presented to confirm the capability of the proposed method.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland