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Research Article | Open Access

Some novel mathematical results on the existence and uniqueness of generalized Caputo-type initial value problems with delay

Pushpendra Kumar1( ), V. Govindaraj1, Zareen A. Khan2( )
Department of Mathematics, National Institute of Technology Puducherry, Karaikal-609609, India
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
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Abstract

In this article, we propose some novel results on the existence and uniqueness of generalized Caputo-type initial value problems with delay by using fixed point theory. The characteristics of space of continuous and measurable functions are the main basis of our results. The proposed results are very useful to prove the existence of a unique solution for the various types of fractional-order systems defined under the generalized Caputo fractional derivative consisting of delay terms.

Keywords

initial value problemgeneralised Caputo fractional derivativedelayexistenceuniqueness
CLC number: 26A33, 34A08, 34A12, 34K12

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AIMS Mathematics
Volume 7 Issue 6,
June 2022
Pages 10483-10494
DOI: 10.3934/math.2022584

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Cite this article:
Kumar P, Govindaraj V, Khan ZA. Some novel mathematical results on the existence and uniqueness of generalized Caputo-type initial value problems with delay. AIMS Mathematics, 2022, 7(6): 10483-10494. https://doi.org/10.3934/math.2022584

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Received: 30 January 2022
Revised: 20 March 2022
Accepted: 23 March 2022
Published: 15 June 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)