Abstract
In this paper, we consider a non-linear sequential differential equation with Caputo fractional derivative of Blasius type and we reduce the problem to the equivalent non-linear integral equation. We prove the complete continuity of the non-linear integral operator. The theorem on the existence of a solution of the problem for the Blasius equation of fractional order is also proved.
Acknowledgements:
The authors are grateful to Professor Mokhtar Kirane for valuable advices during discussions of the results of the present work. The final version of this paper was completed when Berikbol T. Torebek was visiting the University of La Rochelle. The authors would like to thank the editor and referees for their valuable comments and remarks, which led to a great improvement of the article. The second named author is financially supported by a grant from the Ministry of Science and Education of the Republic of Kazakhstan (Grant No.AP05131756).
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