Some novel analysis of two different Caputo-type fractional-order boundary value problems

Nowadays, a number of classical order results are being analyzed in the sense fractional derivatives. In this research work, we discuss two different boundary value problems. first half paper, generalize an integer-order problem into fractional-order and then demonstrate existence uniqueness solution subject to Caputo derivative. First, recall some justify our main with proofs given theorems. We conclude by presenting illustrative example. other extend Banach's contraction theorem prove sequential problem.