Work

Computational and Parameter-Sensitivity Analysis of Dual-Order Memory-Driven Fractional Differential Equations with an Application to Animal Learning

Year: 2025

Type: article

Abstract: Fractional differential equations are used to model complex systems where present dynamics depend on past states. In this work, we study a linear fractional model with two Caputo orders that captures long-term memory together with short-term adaptation. The existence and uniqueness of solutions are established using Banach and Krasnoselskii’s fixed-point theorems. A parameter study isolates the roles of the fractional orders and coefficients, yielding an explicit stability region in the (α,β)–plane via computable contraction bounds. For computation, we implement the Adams–Bashforth–Moulton (ABM) and fractional linear multistep (FLM) methods, comparing accuracy and convergence. As an application, we model animal learning in which proficiency evolves under memory effects and pulsed stimuli. The results quantify the impact of feedback timing on trajectories within the admissible region, thereby illustrating the suitability of dual-order fractional models for memory-driven behavior.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract9100664

Authors: Ali Turab, Josué-Antonio Nescolarde-Selva, Wajahat Ali, Andrés Montoyo, Jun-Jiat Tiang

Institutions: University of Alicante, Northwestern Polytechnical University, University of Ostrava, Multimedia University

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,258