<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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 <italic>n</italic> 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.</p></abstract>

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.

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

Moroccan Journal of Pure and Applied Analysis

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"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...

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

Published Online: Oct 02, 2020

Page range: 168 - 183

DOI: https://doi.org/10.2478/mjpaa-2020-0013

Keywords
Caputo derivative, Lane-Emden equation, Existence of solution, Eixed point, Singular differential equation

© 2020 Yazid Gouari et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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

Published Online: Oct 02, 2020

Page range: 168 - 183

DOI: https://doi.org/10.2478/mjpaa-2020-0013

KeywordsCaputo derivative, Lane-Emden equation, Existence of solution, Eixed point, Singular differential equation

© 2020 Yazid Gouari et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Caputo derivative, Lane-Emden equation, Existence of solution, Eixed point, Singular differential equation