ON WEIGHTED k-FRACTIONAL OPERATORS WITH APPLICATIONS IN MATHEMATICAL PHYSICS

The main objective of this paper is to present weighted k-fractional integral and derivative operators of a function with respect to another function and to uncover their properties. In addition to this, we find the weighted Laplace transform of the newly defined operators. As applications of the weighted k-fractional operators in mathematical physics, we study the fractional forms of kinetic differintegral equation and the time-fractional heat equation involving the novel operators and find their solutions using weighted Laplace transform.