ON THE SOLUTIONS OF FUZZY FRACTIONAL DIFFERENTIAL EQUATION

Year 2014, Volume: 4 Issue: 1, 98 - 103, 01.06.2014

Djurdjica Takaci Arpad Takaci Aleksandar Takaci

Abstract

In this paper the exact and the approximate solutions of fuzzy fractional differential equation, in the sense of Caputo Hukuhara differentiability, with a fuzzy condition are constructed by using the fuzzy Laplace transform. The obtained solutions are expressed in the form of the fuzzy Mittag-Leffler function. The presented procedure is visualized and the graphs of the obtained approximate solutions are drawn by using the GeoGebra package.

Keywords

Fractional, Fuzzy calculus, Laplace transform

References

• Bede1 B., Rudas I.,Bencsik A., (2007), First order linear fuzzy differential equa- tions under generalized differentiability, Journal Information Sciences: an International Journal archive V. 177 I. 7, pp 1648- 1662.
• Arshad S, Lupulescu V., (2011), Fractional differential equation with the fuzzy initial condition, Electronic Journal of Differential Equations, Vol. 2011 No. 34, pp. 1-8.
• Caputo, M., (2008), Linear models of dissipation whose Q is almost frequency independent- II, Geo- phys. J. Royal Astronom. Soc., 13, No 5 (1967), 529-539.
• Kadaka U., Basar,F., (2012), Power series of fuzzy numbers with real or fuzzy coefficients, Filomat 26:3, 519528.
• V. Kiryakova, (2011), Fractional order differential and integral equations with Erd´elyi-Kober opera- tors: Explicit solutions by means of the transmutation method, American Institute of Physics - Conf. Proc. # 1410 (Proc. 37th Intern. Conf. AMEE’ 2011), 247-258; doi: 10.1063/1.3664376.
• V. Kiryakova, (2012), Some operational tools for solving fractional and higher integer order differential equations: A survey on their mutual relations, American Institute of Physics - Conf. Proc. # 1497 (Proc. 38th Intern. Conf. AMEE’ 2012), 273-289; doi: 10.1063/1.4766795.
• Mainardi, F., Yu. Luchko, Pagnini, G., (2001), The fundamental solution of the space-time fractional diffusion equation, Fractional Calculus and its Application, 4,2., 153-192.
• Palash D., Hrishikesh B., Tazid A. (2011), Fuzzy Arithmetic with and without using -cut method: A Comparative Study, International Journal of Latest Trends in Computing (E-ISSN: 2045-5364) 99 Volume 2, Issue 1.
• Salahshour S., Allahviranloo T., Abbasbandy S., (2012), Solving fuzzy fractional differential equations by fuzzy Laplace transforms, Commun Nonlinear Sci Numer Simulat 17, 13721381.
• Takaˇci, Dj., Takaˇci, A., (2007), On the approximate solution of mathematical model of a viscoelastic bar, Nonlinear Analysis, 67, 1560-1569.
• Takaˇci, Dj., Takaˇci, A., ˇStrboja, M., (2010) On the character of operational solutions of the time- fractional diffusion equation, Nonlinear Analysis: 72, 5, 2367-2374.
• J. Tenreiro Machado, V. Kiryakova, (2011), F. Mainardi, Recent history of fractional cal- culus, Communications in Nonlinear Sci. and Numerical Simulations, 16, No 3, 1140-1153; doi:10.1016/j.cnsns.2010.05.027.
• Zadeh, L. A.,Fuzzy Sets, (1965), Information and Control, 8, 338-353.