Solving hybrid functional-fractional equations originating in biological population dynamics with an effect on infectious diseases

Hasanen A. Hammad; Hassen Aydi; Maryam G. Alshehri; Hasanen A. Hammad; Hassen Aydi; Maryam G. Alshehri

doi:10.3934/math.2024709

AIMS Mathematics

2024, Volume 9, Issue 6: 14574-14593. doi: 10.3934/math.2024709

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Research article

Solving hybrid functional-fractional equations originating in biological population dynamics with an effect on infectious diseases

1.
Department of Mathematics, College of Science, Qassim University, Buraydah, 52571, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, Sohag University, Sohag, 82524, Egypt
3.
Institut Supérieur d'Informatique et des Techniques de Communication, Université de Sousse, H. Sousse, 4000, Tunisia
4.
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa
5.
Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box741, Tabuk, 71491, Saudi Arabia

Received: 27 January 2024 Revised: 03 April 2024 Accepted: 09 April 2024 Published: 22 April 2024
MSC : 26A33, 26D15, 47H08, 47H10

This paper study was designed to establish solutions for mixed functional fractional integral equations that involve the Riemann-Liouville fractional operator and the Erdélyi-Kober fractional operator to describe biological population dynamics in Banach space. The results rely on the measure of non-compactness and theoretical concepts from fractional calculus. Darbo's fixed-point theorem for Banach spaces has been utilized. Moreover, the solvability of a specific non-linear integral equation that models the spread of infectious diseases with a seasonally varying periodic contraction rate has been explored by using the Banach contraction principle. Finally, two numerical examples demonstrate the practical application of these findings in the realm of fractional integral equation theory.
- hybrid nonlinear fractional equation,
- infectious diseases,
- Banach space,
- fixed point technique,
- biological population dynamics,
- fractional derivatives
Citation: Hasanen A. Hammad, Hassen Aydi, Maryam G. Alshehri. Solving hybrid functional-fractional equations originating in biological population dynamics with an effect on infectious diseases[J]. AIMS Mathematics, 2024, 9(6): 14574-14593. doi: 10.3934/math.2024709

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Abstract

This paper study was designed to establish solutions for mixed functional fractional integral equations that involve the Riemann-Liouville fractional operator and the Erdélyi-Kober fractional operator to describe biological population dynamics in Banach space. The results rely on the measure of non-compactness and theoretical concepts from fractional calculus. Darbo's fixed-point theorem for Banach spaces has been utilized. Moreover, the solvability of a specific non-linear integral equation that models the spread of infectious diseases with a seasonally varying periodic contraction rate has been explored by using the Banach contraction principle. Finally, two numerical examples demonstrate the practical application of these findings in the realm of fractional integral equation theory.

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