A Study of Complex Financial Dynamics Using Fractal--Fractional Operators with Exponential Memory

A Study of Complex Financial Dynamics Using Fractal--Fractional Operators with Exponential Memory | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 17 November 2025 V1 Latest version Share on A Study of Complex Financial Dynamics Using Fractal--Fractional Operators with Exponential Memory Authors : Mahesh B. Nagpurkar 0009-0000-6869-6946 and Krunal Kachhia 0000-0001-8270-7162 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.176336525.52517641/v1 165 views 148 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract This study introduces a novel financial model based on fractal–fractional calculus with exponential decay kernels and Riemann-type derivatives, designed to capture memory-dependent processes and erratic time dynamics inherent in financial systems. The model effectively describes the dynamic interplay among three critical economic variables: price indices, investment demand and interest rates. Using a newly developed predictor–corrector numerical scheme tailored for fractal–fractional operators, we analyze the system’s local and global behavior, including equilibrium structure and Lyapunov spectra. The results reveal the presence of chaotic dynamics, driven by the fractional order µ and fractality index ν . Parametric analysis confirms that varying these parameters transitions the system from stability to chaos. This modeling approach offers a versatile and powerful framework for capturing nonlinear feedback, memory and multiscale characteristics of complex financial phenomena. Supplementary Material File (mahesh_krunal_finance_latest_1007 (9).pdf) Download 2.42 MB Information & Authors Information Version history V1 Version 1 17 November 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords chaotic financial dynamics financial modeling fractal–fractional derivatives predictor–corrector method Authors Affiliations Mahesh B. Nagpurkar 0009-0000-6869-6946 P D Patel Institute of Applied Sciences View all articles by this author Krunal Kachhia 0000-0001-8270-7162 [email protected] P D Patel Institute of Applied Sciences View all articles by this author Metrics & Citations Metrics Article Usage 165 views 148 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Mahesh B. Nagpurkar, Krunal Kachhia. A Study of Complex Financial Dynamics Using Fractal--Fractional Operators with Exponential Memory. Authorea . 17 November 2025. DOI: https://doi.org/10.22541/au.176336525.52517641/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . 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