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 Gr"{o}wnwall rule for singular kernels of the equations helps to show our findings are correct. We confirm our findings by giving a few practical examples.
Samei,M. E. and Hatami,A. (2023). To numerical explore a fractional implicit $Q$-differential equations with Hilfer type and via nonlocal conditions. Mathematical Analysis and Convex Optimization, 4(1), 97-117. doi: 10.22034/maco.4.1.9
MLA
Samei,M. E. , and Hatami,A. . "To numerical explore a fractional implicit $Q$-differential equations with Hilfer type and via nonlocal conditions", Mathematical Analysis and Convex Optimization, 4, 1, 2023, 97-117. doi: 10.22034/maco.4.1.9
HARVARD
Samei M. E., Hatami A. (2023). 'To numerical explore a fractional implicit $Q$-differential equations with Hilfer type and via nonlocal conditions', Mathematical Analysis and Convex Optimization, 4(1), pp. 97-117. doi: 10.22034/maco.4.1.9
CHICAGO
M. E. Samei and A. Hatami, "To numerical explore a fractional implicit $Q$-differential equations with Hilfer type and via nonlocal conditions," Mathematical Analysis and Convex Optimization, 4 1 (2023): 97-117, doi: 10.22034/maco.4.1.9
VANCOUVER
Samei M. E., Hatami A. To numerical explore a fractional implicit $Q$-differential equations with Hilfer type and via nonlocal conditions. MACO, 2023; 4(1): 97-117. doi: 10.22034/maco.4.1.9
Mathematical Analysis and Convex Optimization