2013/05/14 by Sun-Ae Pak, Sunae Pak, Pak, Sun-Ae +5
Mathematics · #26A33 #34A08 #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #math.CA #msc:26A33 #msc:34A08
paper · pdf · doi:10.48550/arxiv.1305.3193
22 pages
arxiv created 2013/05/14 · openalex publication_date 2013/05/14 · arxiv updated 2013/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the canonical fundamental systems of solutions of linear homogeneous Caputo fractional differential equations with continuous variable coefficients. Here we gained a series-representation of the canonical fundamental system by coefficients of the considered equations and the representation of solution to initial value problems using the canonical fundamental system. According to our results, the canonical fundamental system of solutions to linear homogeneous differential equation with Caputo fractional derivatives and continuous variable coefficients has different representations according to the distributions of the lowest order of the fractional derivatives in the equation and the distance from the highest order to its adjacent order of the fractional derivatives in the equation.