Existence of positive solutions for weighted fractional order differential equations

•The article deals with a generalized type of fractional dynamic equation and hence many results in literature can be re-covered by our results.•By different choices of the weight function several types of equations are studied.•Numerical examples are given for more generalized kernels.•Nonlinear analysis methods are utilized to study the existence and uniqueness of weighted generalized fractional equations in the Caputo sense.•New function spaces are used to deal with the used weight function. In this paper, we deliberate two classes of initial value problems for nonlinear fractional differential equations under a version weighted generalized of Caputo fractional derivative given by Jarad et al. (2020a) [25]. We get a formula for the solution through the equivalent fractional integral equations to the proposed problems. The existence and uniqueness of positive solutions have been obtained by using lower and upper solutions. The acquired results are demonstrated by building the upper and lower control functions of the nonlinear term with the aid of Banach and Schauder fixed point theorems. The acquired results are demonstrated by pertinent numerical examples along with the Bashforth Moulton prediction correction scheme and Matlab.