NUMERICAL ANALYSIS OF MEMORY EFFECT IN CAPUTO FRACTIONAL COOLING MODELS VIA EULER TYPE METHODS

SALIHI, Ylldrita and RASIMI, Krutan and Shemshi, Vjollca and Sejfuli-Ramadani, Nexhibe (2026) NUMERICAL ANALYSIS OF MEMORY EFFECT IN CAPUTO FRACTIONAL COOLING MODELS VIA EULER TYPE METHODS. In: INTERNATIONAL CONFERENCE “FROM RESEARCH TO APPLICATION”, 20 May, 2026.

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Abstract

Fractional differential equations have attracted significant attention due to their ability to model memory- dependent phenomena. In this paper, we study the numerical solution of a Caputo-type fractional differential equation using the L1 discretization scheme, comparing the explicit Forward Euler and implicit Backward Euler methods in terms of accuracy and stability. The problem is studied on [0,5] with y(0)=0, using an interactive analysis to visualize and assess accuracy against the exact solution. A systematic analysis is performed for different discretization step sizes h h h    0.1, 0.01, 0.001 and fractional orders   0.8, 0.9, 0.999 . The visualization is carried out separately for varying  with fixed step size h, and, conversely, with step size varied at fixed  , to analyze the memory effect. The maximum error is presented in a log–log plot, while the Caputo L1 weights (Euler weights) are analyzed to illustrate the memory effect, summarized in tables for comparison and stability analysis of the solution. The comparison shows that the implicit Backward Euler method performs better in terms of stability and accuracy, especially when larger step sizes are used. Overall, the numerical results obtained in Mathematica suggest that implicit time-discretization methods are a reliable and robust choice for solving fractional differential equations, particularly when stability is important.

Item Type: Conference or Workshop Item (Paper)
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Engineering, Science and Mathematics > School of Mathematics
Depositing User: Unnamed user with email zshi@unite.edu.mk
Date Deposited: 21 Sep 2026 12:05
Last Modified: 21 Sep 2026 12:05
URI: http://eprints.unite.edu.mk/id/eprint/2421

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