EXISTENCE OF SOLUTION FOR A HILFER FRACTIONAL DIFFERENTIAL EQUATION USING COINCIDENCE DEGREE THEORY

We have used Mawhin’s coincidence degree theory to study the existence of a positive solution for the Hilfer fractional differential equation with Riemann-Stieltjes integral boundary conditions. Our problem is considered at resonance. Utilizing the required function spaces, norms, and operators, we establish specific conditions to prove our results on the existence of solutions. We have included two examples to demonstrate our findings. A discussion section is also provided, examining potential avenues for future research.