Algebraic reduction of fractional systems: Analytical solutions and memory-induced soliton deformation

Inga Telksnienė, Tadas Telksnys, Romas Marcinkevičius, Zenonas Navickas, Raimondas Čiegis and Minvydas Ragulskis

Chaos, Solitons & Fractals, 2026, vol. 210, issue P1

Abstract: This study presents a novel algebraic methodology that transforms systems of nonlinear Caputo fractional differential equations into equivalent first-order ordinary differential equations. By applying the properties of fractional power series, the proposed framework maps non-local fractional operators directly into a local integer-order domain, embedding infinite memory effects into a deterministic, time-dependent polynomial forcing term. The physical applicability of this reduction technique is investigated through the analysis of a multiplicatively coupled fractional Riccati system, specifically focusing on the deformation of solitary wave solutions induced by fractional memory. Computational experiments indicate that non-zero fractional initial conditions function as continuous shape modulators that fundamentally alter the amplitude, width, and asymptotic decay rates of solitary waves, thereby breaking the exact symmetries of standard localized behavior. Despite this memory-induced deformation and the associated loss of general integrability, novel exact analytical solutions are successfully constructed for the perturbed system. By identifying specific parameter constraints that compensate for the non-autonomous memory effects, the nonlinear ordinary differential equation system is mapped into a higher-dimensional linear space and resolved using Bessel functions. The resulting closed-form analytical solutions, represented as exact integrals, are validated against direct numerical approximation methods, confirming the accuracy and practical utility of the proposed mathematical framework for analyzing complex fractional dynamics.

Keywords: Caputo fractional derivative; Fractional power series; Fractional Riccati system; Solitary waves; Memory effects; Exact analytical solutions (search for similar items in EconPapers)
Date: 2026
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077926007496
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:210:y:2026:i:p1:s0960077926007496

DOI: 10.1016/j.chaos.2026.118608

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().