SOLUSI PERSAMAAN DIFERENSIAL FRAKSIONAL LINIER HOMOGEN DENGAN METODE MITTAG-LEFFLER

Helfa Oktafia Afisha; Yuni Yulida; Nurul Huda

doi:10.20527/epsilon.v10i1.53

SOLUSI PERSAMAAN DIFERENSIAL FRAKSIONAL LINIER HOMOGEN DENGAN METODE MITTAG-LEFFLER

Helfa Oktafia Afisha, Yuni Yulida, Nurul Huda

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 𝑦𝑦 (𝑥𝑥) = 𝐸𝐸αα (𝑏𝑏𝑏 αα) = 􀷍𝑏𝑏𝑘𝑘𝑥𝑥𝑘𝑘𝑘 Γ (𝑘𝑘𝑘𝑘 + 1) ∞𝑘𝑘 = 0 This series converges for 𝑥𝑥 at 􁉀-1𝑏𝑏, 1𝑏𝑏􁉁. The derivative search of 𝑦𝑦 (𝑥𝑥), is done by deriving each term from 𝑦𝑦 (𝑥𝑥) using the definition of Caputo derivative followed by determining the coefficient 𝑏𝑏𝑘𝑘 to obtain the PDF solution.

Keywords

Fractional Calculus, Mittag-Leffler Function and Fractional Differential Equations

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DOI: https://doi.org/10.20527/epsilon.v10i1.53