A POWER SERIES METHOD FOR THE FUZZY FRACTIONAL LOGISTIC DIFFERENTIAL EQUATION

Babak Shiri (), Zahra Alijani () and Yeliz Karaca
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Babak Shiri: Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, P. R. China
Zahra Alijani: Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, Ostrava 702 00, Czech Republic
Yeliz Karaca: University of Massachusetts Chan Medical School (UMASS), 55 Lake Avenue North, Worcester, MA 01655, USA

FRACTALS (fractals), 2023, vol. 31, issue 10, 1-11

Abstract: Power series, as an important means to analyze functions in different complex settings, are employed in various applied areas to solve differential equations and nonlinear problems and provide the assessment of intervals of convergence. Accordingly, the fuzzy logistic differential equation using the Caputo operator has been studied in this paper. Accordingly, the fuzzy logistic differential equation using the Caputo operator has been studied in this paper. The generalized Hukuhara difference and the generalized Hukuhara derivative are also used, and a power series representation is proposed for the solution of the fuzzy fractional logistic equation. Afterward, power series coefficients are obtained using a recursive formula. Finally, numerical experiments and illustrated results of the computations are presented to allow for more realistic decisions reflecting high complexity and underlying uncertainty. Thus, the numerical computations in our study reveal the effectiveness and accuracy of the power series method. Therefore, it is found that the fuzzy solution converges to the deterministic solution when uncertainty decreases, and, based on the technical analyses, it has been demonstrated that the results obtained are more fundamental in preventing geometric growth in nonlinear phenomena where uncertainties emerge due to impreciseness and inexactness.

Keywords: Power Series Method; Logistic Equation; Fuzzy Fractional Logistic Differential Equation; Caputo Fractional Derivative; Fuzzy Fractional Initial Value Problem; Hukuhara Derivative; Nonlinear Numerical Computations; Impreciseness and Inexactness (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S0218348X23400868

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