Abstract
Abstract The heat conduction equation is considered in a composite body consisting of two regions: 0 < x < L and − L < x < 0. Heat conduction in one region is described by the equation with the Caputo fractional derivative of order α, whereas in another region by the equation with the Caputo fractional derivative of order β. The integral transforms technique is used. The approximate solution valid for small values of time is analyzed in detail.
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