TO NUMERICAL EXPLORE A FRACTIONAL IMPLICIT Q-DIFFERENTIAL EQUATIONS WITH HILFER TYPE AND VIA NONLOCAL CONDITIONS

This paper tries to show that there is only one solution for problem of fractional q-differential equations with Hilfer type, and it does so by using a particular method known as Schaefer’s fixed point theorem and the Banach contraction principle. After that, we create a integral type of the problem for nonlocal condition. Next, we show that Ulam stability is true. The Gröwnwall rule for singular kernels of the equations helps to show our findings are correct. We confirm our findings by giving a few practical examples.