Abstract:
A linear inhomogeneous equation in a Banach space on the real axis, solved with respect to the fractional Liouville derivative, with a bisectorial
operator at the unknown function is investigated. The equation is considered without initial
conditions. Using the theory of the Fourier transform, the existence
of a unique solution to the equation is proved. It is shown that the solution has the form of the convolution of the inverse
Fourier transform of the bisectorial operator resolvent and the right-hand side of
the equation. Abstract results are applied to study some classes of
partial differential equations and systems of equations with a fractional derivative with respect to a
selected variable.
Keywords:fractional Liouville derivative, equation on the real axis without initial
conditions, bisectorial operator, Fourier transform, boundary value problem.
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