SOLUSI PERSAMAAN DIFERENSIAL FRAKSIONAL LINIER HOMOGEN DENGAN METODE MITTAG-LEFFLER - Helfa Oktafia Afisha; Yuni Yulida; Nurul Huda (Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat, 2016)
The classical calculus only studies derivatives as well as differential equations of integers, whereas for non-integral integers and differential equations are not included. Thus the concept of fractional calculus, which studies the integral and non-integral order of abbreviated diferintegral including fractional differential equations (PDF). In this paper we present a method for obtaining a homogeneous linear PDF solution built in the Mittag-Leffler function in the form of a series ???????? (????????) = ????????αα (???????????? αα) = ???????????????????????????????????????? Γ (???????????????? + 1) ∞???????? = 0 This series converges for ???????? at ????-1????????, 1????????????. The derivative search of ???????? (????????), is done by deriving each term from ???????? (????????) using the definition of Caputo derivative followed by determining the coefficient ???????????????? to obtain the PDF solution.