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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.

MSC:
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
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