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

By W. Kavitha Williams, V. Vijayakumar, R. Udhayakumar, Kottakkaran Sooppy Nisar. Numerical Methods for Partial Differential Equations, 2020

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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.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/98cb79a76ae29a0f4081d25dd4846973c78441cd

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In Applied Mathematics

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

New discussion on approximate controllability results for fractional Sobolev type Volterra‐Fredholm integro‐differential systems of order 1 < r < 2 (2021, background): “The studies about existence and controllability related to fractional evolution system of order 1 𝛼 2 attracted many researchers and one can review the articles [10, 17, 25–33].”