Granular Fuzzy Fractional Financial Systems Governed by Granular Caputo Fractional Derivative

Feryal Abdullah Aladsani, Ghulam Muhammad () and Sayed K. Elagan
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Feryal Abdullah Aladsani: Department of Mathematics and Statistics, College of Science, King Faisal University, Hafuf 31982, Al Ahsa, Saudi Arabia
Ghulam Muhammad: Department of Mathematics, Lahore Garrison University, Lahore 54000, Pakistan
Sayed K. Elagan: Department of Mathematics and Computer Sciences, Faculty of Science, Menoufia University, Shebin Elkom 32511, Egypt

Mathematics, 2025, vol. 13, issue 8, 1-24

Abstract: A granular fuzzy fractional financial system (GFFFS) is important for modeling real-world market uncertainties and complexities compared to conventional financial models. Unlike traditional approaches, a GFFFS offers enhanced precision in risk assessment, captures the long-term memory effects with the fractional derivatives, and effectively deals with the uncertainty and granularity in financial data through fuzzy logic. This model overcomes the limitations of the traditional model by accurately representing nonlinear dynamics, extreme volatility, and uncertain behavioral shifts in financial markets. The study of such models can be complex and challenging. However, developing an effective technique for solving such systems analytically and approximately is essential. This article aims to introduce and investigate a GFFFS using granular Caputo fractional derivatives. The behavior of the proposed model is studied using two distinct approaches, including an analytical approach, by applying the fuzzy Laplace transform technique and a numerical approach by employing fuzzy integral equations. Moreover, the existence and uniqueness of the extracted fuzzy solution are determined using the Banach contraction principle. To analyze the nonlinearity of the proposed model, the introduced numerical scheme is employed to illustrate the uncertain behavior of the proposed model graphically. This research provides deeper insights that can help decision-makers make better financial market decisions.

Keywords: granular Caputo fractional derivative; granular fuzzy fractional financial system; fuzzy Laplace transform; existence and uniqueness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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