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A generalized sequential problem of Lane-Emden type via fractional calculus

In this paper, we combine the Riemann-Liouville integral operator and Caputo derivative to investigate a nonlinear time-singular differential equation of Lane Emden type. The considered problem involves n fractional Caputo derivatives under the conditions that neither commutativity nor semi group property is satisfied for these derivatives. We prove an existence and uniqueness analytic result by application of Banach contraction principle. Then, another result that deals with the existence of at least one solution is delivered and some sufficient conditions related to this result are established by means of the fixed point theorem of Schaefer. We end the paper by presenting to the reader some illustrative examples.

Auteur(s) : Yazid Gouari, Zoubir Dahmani, Ameth Ndiaye
Pages : 168-183
Année de publication : 2020
Revue : Moroccan Journal of Pure and Applied Analysis
N° de volume : 6
Type : Article
Mise en ligne par : NDIAYE Ameth