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An extension of Krasnoselskii’s fixed point theorem and its application to nonlocal problems for implicit fractional differential systems with uncertainty

Authors: 

Hoang Viet Long and Nguyen Phuong Dong

Source title: 
Journal of Fixed Point Theory and Application, 20:37, 2018 (ISI)
Academic year of acceptance: 
2018-2019
Abstract: 

The traditional Krasnoselskii’s fixed point theorem in Banach spaces does not reproduce the rich and varied forms of operator equations in abstract spaces which are not linear structure. Consequently, its applications to integral equations and differential equations have met many obstacles. The present alternative Krasnoselskii’s fixed point theorem in generalized semilinear Banach spaces overcomes this deficiency and opens up for profitable investigation such as differential systems with uncertainty. An application to the existence of solutions of nonlocal problems for fuzzy implicit fractional differential systems under Caputo generalized Hukuhara differentiability with demonstrated example is given to validate the effectiveness of our theoretical results.