Uncertain dynamic responses of fuzzy fractionally damped spring-mass system

Article type: Research Article

Authors: Chakraverty, S | Behera, Diptiranjan^*

Affiliations: Department of Mathematics, National Institute of Technology Rourkela, Odisha, India

Correspondence: [*] Correspondence to: Diptiranjan Behera, Department of Mathematics, National Institute of Technology Rourkela, Odisha769 008, India. Tel.: +91 661 2462713; Fax: +91 661 2462713 2701; diptiranjanb@gmail.com

Abstract: This paper investigates the numerical solution of imprecisely defined fractional order dynamic system, subjected to a unit step load. A mechanical spring-mass system having fractional damping of order 1/2 with fuzzy initial condition is taken into consideration. Fuzziness appeared in the initial conditions are modelled through Gaussian convex normalised fuzzy sets. Homotopy Perturbation Method (HPM) is used with fuzzy based approach to obtain the uncertain dynamic response. Numerical examples related to this are solved by symbolic computations. Obtained results are depicted in term of plots to show the efficacy and powerfulness of the methodology.

Keywords: Fuzzy fractional order dynamic systems, homotopy perturbation method, Caputo derivative, Mittage-Leffler function, Gaussian fuzzy number

DOI: 10.3233/IFS-151598

Journal: Journal of Intelligent & Fuzzy Systems, vol. 29, no. 1, pp. 327-336, 2015