Positive Green's functions for some fractional-order boundary value\n problems

2014/11/20 by Douglas R. Anderson, Anderson, Douglas R.
Mathematics · #26A33 #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.1411.5616

openalex publication_date 2014/11/20 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28

Abstract

We use the newly introduced conformable fractional derivative, which is\ndifferent from the Caputo and Riemann-Liouville fractional derivatives, to\nreformulate several common boundary value problems, including those with\nconjugate, right-focal, and Lidstone conditions. With the fractional\ndifferential equation and fractional boundary conditions established, we find\nthe corresponding Green's functions and prove their positivity under\nappropriate assumptions.\n

Citations

• A New Fractional Derivative with Classical Properties

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