zbMATH — the first resource for mathematics

An equation with left and right fractional derivatives. (English) Zbl 1246.26008
Summary: We consider an equation with left and right fractional derivatives and with the boundary condition \(y(0) = \lim_{x\to 0+} y(x) = 0\), \(y(b) = \lim_{x\to b-} y(x) = 0\) in the space \(L^1(0, b)\) and in the subspace of tempered distributions. The asymptotic behavior of solutions in the end points 0 and \(b\) have been specially analyzed by using Karamata’s regularly varying functions.

26A33 Fractional derivatives and integrals
26A12 Rate of growth of functions, orders of infinity, slowly varying functions
34B99 Boundary value problems for ordinary differential equations
Full Text: DOI