  Initial value problem involving Atangana-Baleanu derivative is considered. An
Explicit solution of the given problem is obtained by reducing the differential
equation to Volterra integral equation of second kind and by using Laplace
transform. To find the solution of the Volterra equation, the successive
approximation method is used and a lemma simplifying the resolvent kernel has
been presented. The use of the given initial value problem is illustrated by
considering a boundary value problem in which the solution is expressed in the
form of series expansion using orthogonal basis obtained by separation of
variables.
