  The present study is based on a generalized form of Brans-Dicke (BD) theory
where, the dimensionless BD parameter is regarded as a function of the scalar
field, which is reciprocal of the gravitational constant. The field equations
have been solved by incorporating an empirical function f(t) in the expression
representing the conservation of matter. This function f(t) has been chosen to
account for a conversion of matter (both dark and baryonic) into some other
form, possibly dark energy, which is known to be responsible for the
accelerated expansion of universe. The requirement of a signature flip of the
deceleration parameter (q), which is evident from other studies, sets the
boundary conditions to be satisfied by the function f(t), leading to the
formulation of its time dependence. A simple empirical relation was initially
assumed to represent the time dependence of f(t), and the constants in this
expression have been determined from these boundary conditions. The BD
parameter has been found to have a negative value throughout the range of
study. The dependence of BD parameter upon the scalar field has been depicted
graphically. A smooth transition of the universe, from a decelerated to an
accelerated phase of expansion, is found to occur due to a conversion of matter
into dark energy. The gravitational constant is found to be increasing with
time.
