An Extensive Study of Weighted Hilfer Fractional Calculus With Respect to Functions

This research contributes to the field of fractional calculus in theoretical sense. We investigate a new operator, proposed by combing the already known Hilfer operator and weighted operator with respect to functions, in terms of some fundamental properties. These properties include composition properties, boundedness, convergence, and mapping in two different function spaces. Lastly, we discuss fractional differential equations involving these operators and establish conditions for existence, uniqueness, and stability by using concepts from fixed point theory.