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All Journal Epsilon: Jurnal Matematika Murni dan Terapan
Helfa Oktafia Afisha
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Decision Sciences, Operations Research & Management Transportation

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SOLUSI PERSAMAAN DIFERENSIAL FRAKSIONAL LINIER HOMOGEN DENGAN METODE MITTAG-LEFFLER Helfa Oktafia Afisha; Yuni Yulida; Nurul Huda
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 10, No 1 (2016): JURNAL EPSILON VOLUME 10 NOMOR 1
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (223.837 KB) | DOI: 10.20527/epsilon.v10i1.53

Abstract

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.
Co-Authors Nurul huda Yuni Yulida