{'fraction_non_alphanumeric': 0.05263157894736842, 'fraction_numerical': 0.007177033492822967, 'mean_word_length': 4.819444444444445, 'pattern_counts': {'":': 0, '<': 2, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Periodic problem for two-term fractional differential equations

Abstract We discuss the existence, multiplicity and uniqueness of solutions to the periodic problem cDαu + q(t,u)cDβu = f(t,u), u(0) = u(T), where 0 < β < α ≤ 1. The existence results are proved by the combination of the Schauder fixed point theorem with the maximum principle for the Caputo fractional derivative and the structure of compact sets in ℝ.