A new study on existence and uniqueness of nonlocal fractional delay differential systems of order 1 < r < 2 in Banach spaces

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Abstract
This article is mainly focusing on the existence and uniqueness of nonlocal fractional delay differential systems of order 1 < r < 2 in Banach spaces. By using the theoretical concepts related to the fractional calculus, cosine, and sine functions of operators and fixed point approach, we prove our main results. By using Kranoselskii's fixed point theorem, we discuss the existence of the mild solution and by applying the Banach contraction principle, we prove the existence and uniqueness of the mild solution of nonlocal fractional delay differential system. Finally, we provide an example to illustrate the obtained theoretical results.

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