An equation with left and right fractional derivatives. (English) Zbl 1246.26008

Stanković, B.

Publ. Inst. Math., Nouv. Sér. 80(94), 259-272 (2006).

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

Keywords:

right and left Riemann-Liouville fractional derivative; fractional differential equation; regularly varying functions