Analysis of a nonlinear problem involving discrete and proportional delay with application to Houseflies model

Kamal Shah; Muhammad Sher; Muhammad Sarwar; Thabet Abdeljawad; Kamal Shah; Muhammad Sher; Muhammad Sarwar; Thabet Abdeljawad

doi:10.3934/math.2024355

AIMS Mathematics

2024, Volume 9, Issue 3: 7321-7339. doi: 10.3934/math.2024355

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Analysis of a nonlinear problem involving discrete and proportional delay with application to Houseflies model

1.
Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
2.
Department of Mathematics, University of Malakand, Chakdara Dir(L), 18000, Khyber Pakhtunkhwa, Pakistan
3.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan
4.
Department of Mathematics Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Korea
5.
Department of Mathematics and Applied Mathematics School of Science and Technology, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa

Received: 02 January 2024 Revised: 23 January 2024 Accepted: 04 February 2024 Published: 20 February 2024
MSC : 26A33, 34A08, 34A12

This manuscript established a comprehensive analysis of a general class of fractional order delay differential equations with Caputo-Fabrizio fractional derivative (CFFD). Functional analysis was used to examine the existence and uniqueness of the suggested class and to generate sufficient requirements for Ulam-Hyers (UH) type stability. Further, a numerical method based on Lagrange interpolation is used to compute approximate solution. Then, some applications in physical dynamics including a houseflies model and a Cauchy type problem were discussed to illustrate the established analysis with graphical illustrations.
- CFFD,
- existence theory,
- UH stability,
- numerical results
Citation: Kamal Shah, Muhammad Sher, Muhammad Sarwar, Thabet Abdeljawad. Analysis of a nonlinear problem involving discrete and proportional delay with application to Houseflies model[J]. AIMS Mathematics, 2024, 9(3): 7321-7339. doi: 10.3934/math.2024355

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Abstract

This manuscript established a comprehensive analysis of a general class of fractional order delay differential equations with Caputo-Fabrizio fractional derivative (CFFD). Functional analysis was used to examine the existence and uniqueness of the suggested class and to generate sufficient requirements for Ulam-Hyers (UH) type stability. Further, a numerical method based on Lagrange interpolation is used to compute approximate solution. Then, some applications in physical dynamics including a houseflies model and a Cauchy type problem were discussed to illustrate the established analysis with graphical illustrations.

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