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Weak solutions to differential equations with left and right fractional derivatives defined on \(R\). (English) Zbl 1274.26012

Summary: We treat linear differential equations containing both left and right Riemann-Liouville fractional derivatives arising from fractional variational problems. We use the Fourier transform method to obtain a weak solution to the problem. The regularity of such solution is examined and the conditions for the existence of a classical solution are stated.

MSC:

26A33 Fractional derivatives and integrals
34A08 Fractional ordinary differential equations
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