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Existence results of a nonlocal impulsive fractional stochastic differential systems with Atangana–Baleanu derivative

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The study of this work ensures the existence results of a class of Atangana–Baleanu (A–B) fractional stochastic differential equations with non-instantaneous impulses and nonlocal conditions. For this investigation, the proposed fractional impulsive stochastic system is transformed into an equivalent fixed point problem. The operator is then analyzed for boundedness, contraction, continuity and equicontinuity. Then Arzela–Ascolli theorem ensures the operator is relatively compact and Krasnoselskii’s fixed point theorem is proved for the existence of the mild solution. At last, to verify the theoretical results an example is given. The obtained result suggest that the proposed method is efficient and proper for dealing with the fractional stochastic problems arising in engineering, technology and physics, and in terms of the A–B fractional derivative.

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We are very thankful to the anonymous reviewers and associate editor for their constructive comments and suggestions which help us to improve the manuscript.

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Authors and Affiliations



Rajesh Dhayal: conceptualization, methodology, formal analysis, writing original draft; Mohd Nadeem: supervision, writing review and editing, formal analysis. All authors read and approved the final manuscript.

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Correspondence to Rajesh Dhayal.

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Communicated by S. Ponnusamy.

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Dhayal, R., Nadeem, M. Existence results of a nonlocal impulsive fractional stochastic differential systems with Atangana–Baleanu derivative. J Anal (2024).

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