  In this paper, we delve into the fascinating realm of fractal calculus
applied to fractal sets and fractal curves. Our study includes an exploration
of the method analogues of the separable method and the integrating factor
technique for solving $\alpha$-order differential equations. Notably, we extend
our analysis to solve Fractal Bernoulli differential equations. The
applications of our findings are then showcased through the solutions of
problems such as fractal compound interest, the escape velocity of the earth in
fractal space and time, and estimation of time of death incorporating fractal
time. Visual representations of our results are also provided to enhance
understanding.
