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

Pushpendra Kumar; V. Govindaraj; Zareen A. Khan; Pushpendra Kumar; V. Govindaraj; Zareen A. Khan

doi:10.3934/math.2022584

AIMS Mathematics

2022, Volume 7, Issue 6: 10483-10494. doi: 10.3934/math.2022584

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Research article

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

1.
Department of Mathematics, National Institute of Technology Puducherry, Karaikal-609609, India
2.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia

Received: 30 January 2022 Revised: 20 March 2022 Accepted: 23 March 2022 Published: 28 March 2022
MSC : 26A33, 34A08, 34A12, 34K12

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.
- initial value problem,
- generalised Caputo fractional derivative,
- delay,
- existence,
- uniqueness
Citation: Pushpendra Kumar, V. Govindaraj, Zareen A. Khan. Some novel mathematical results on the existence and uniqueness of generalized Caputo-type initial value problems with delay[J]. AIMS Mathematics, 2022, 7(6): 10483-10494. doi: 10.3934/math.2022584

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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.

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