Analysis of hybrid fractional integro-differential equations with application to cholera dynamics

• Published in: Scientific reports Vol. 15; no. 1; pp. 33905 - 15
• Main Authors: Algolam, Mohamed S., Chebab, Mesbah, Abdo, Mohammed S., Alshammari, Fahdah, Aldwoah, Khaled
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 30.09.2025; Nature Publishing Group; Nature Portfolio
• Subjects: 639/705; 639/705/1041; 692/699; Adams-Bashforth method; Algebra; Boundary conditions; Calculus; Cholera; Cholera model; Dhage theorem; Differential equations; Epidemic models; Epidemics; Epidemiology; Humanities and Social Sciences; Hybrid integro-differential equation; Integral equations; Mathematical functions; multidisciplinary; Science; Science (multidisciplinary); Slit-strip boundary conditions; vartheta$$ -Caputo fractional operators; Waterborne diseases; Slit-strip boundary conditions; Adams-Bashforth method; Caputo fractional operators; Hybrid integro-differential equation; Dhage theorem; Cholera model; ϑ-Caputo fractional operators
• ISSN: 2045-2322; 2045-2322
• DOI: 10.1038/s41598-025-10159-y

This study establishes the existence of solutions for a class of fractional hybrid integro-differential equations governed by the -Caputo derivative, subject to slit-strip boundary conditions. The significance of this work lies in the integration of advanced fractional calculus, specifically, the -Caputo operator, with a biologically meaningful cholera epidemic model. Using Dhage’s fixed point theorem, we rigorously prove the existence of solutions, distinguishing this work from existing models based solely on standard fractional derivatives. Two illustrative examples are presented, including a novel cholera model that captures memory effects, environmental feedback, and nonlinear transmission pathways. Numerical simulations, implemented via the Adams-Bashforth-Moulton method, demonstrate how variations in the fractional-order parameter influence the disease dynamics over time. These results underscore the value of fractional modeling in capturing real-world epidemic behaviors and support the use of the -Caputo framework in future epidemiological studies.