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Positive solutions of nonlinear fractional differential equations in non-zero self-distance spaces

  • Hemant Kumar Nashine ORCID logo , Anita Gupta and Ravi P. Agarwal ORCID logo EMAIL logo
Published/Copyright: October 24, 2017
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Abstract

This paper is concerned with the existence of positive solutions of three classes of nonlinear fractional differential equations using fixed point results in non-zero self-distance spaces. We introduce new concepts of generalized α-weakly (ψ,φ)s-contractive mappings involving rational terms and then develop fixed point results for weakly α-admissible mappings. Some new examples and counterexamples are given to illustrate the applicability and effectiveness of these results over existing ones. In that way, we extend some previous results. For applications to fractional q-difference boundary value problems, the use of a p-Laplacian operator is suggested.

MSC 2010: 47H10; 34A08

Award Identifier / Grant number: 2052/FNPDR/2015

Funding statement: The first author is thankful to the United State-India Education Foundation, New Delhi, India and IIE/CIES, Washington, DC, USA for Fulbright-Nehru PDF Award (no. 2052/FNPDR/2015).

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Received: 2016-7-31
Accepted: 2016-12-22
Published Online: 2017-10-24
Published in Print: 2017-12-1

© 2017 Walter de Gruyter GmbH, Berlin/Boston

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