Inverse source problem for the abstract fractional differential equation
Andrey B. Kostin, Sergey Piskarev
Abstract
Abstract In a Banach space, the inverse source problem for a fractional differential equation with Caputo–Dzhrbashyan derivative is considered. The initial and observation conditions are given by elements from <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>D</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>A</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:math> {D(A)} , and the operator function on the right side is sufficiently smooth. Two types of the observation operator are considered: integral and at the final point. Under the assumptions that operator A is a generator of positive and compact semigroup the uniqueness, existence and stability of the solution are proved.