Open Access

ARTICLE

A Study on the Nonlinear Caputo-Type Snakebite Envenoming Model with Memory

Pushpendra Kumar^1,*, Vedat Suat Erturk², V. Govindaraj¹, Dumitru Baleanu^3,4,5

1 Department of Mathematics, National Institute of Technology Puducherry, Karaikal, 609609, India
2 Department of Mathematics, Faculty of Arts and Sciences, Ondokuz Mayis University, Atakum, Samsun, 55200, Turkey
3 Department of Mathematics, Cankaya University, Ankara, 06530, Turkey
4 Institute of Space Sciences, Magurele, Bucharest, R76900, Romania
5 Department of Computer Science and Mathematics, Lebanese American University, Beirut, 11022801, Lebanon

* Corresponding Author: Pushpendra Kumar. Email:

(This article belongs to the Special Issue: Advanced Numerical Methods for Fractional Differential Equations)

Computer Modeling in Engineering & Sciences 2023, 136(3), 2487-2506. https://doi.org/10.32604/cmes.2023.026009

Received 09 August 2022; Accepted 10 November 2022; Issue published 09 March 2023

Abstract

In this article, we introduce a nonlinear Caputo-type snakebite envenoming model with memory. The well-known Caputo fractional derivative is used to generalize the previously presented integer-order model into a fractional-order sense. The numerical solution of the model is derived from a novel implementation of a finite-difference predictor-corrector (L1-PC) scheme with error estimation and stability analysis. The proof of the existence and positivity of the solution is given by using the fixed point theory. From the necessary simulations, we justify that the first-time implementation of the proposed method on an epidemic model shows that the scheme is fully suitable and time-efficient for solving epidemic models. This work aims to show the novel application of the given scheme as well as to check how the proposed snakebite envenoming model behaves in the presence of the Caputo fractional derivative, including memory effects.

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Keywords

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