SOLVABILITY OF SEQUENTIAL FRACTIONAL DIFFERENTIAL EQUATIONS WITH FUNCTIONAL BOUNDARY VALUE CONDITIONS

The purpose of this paper is to develop the existence theory for a functional boundary problem of sequential fractional differential equations involving Caputo fractional derivatives of order $ \alpha+1 $ with $ n-1<\alpha\leq n $. The main goal of the current contribution is to use Mawhin's coincidence degree theory and a few novel operators to derive sufficient criteria for the existence of solutions to the resonance problems at hand. An example that is relevant is given to support the findings.