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Analysis on the solution of fractional fuzzy differential equations

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Abstract

This article is concerned with an appropriate definition of the fractional derivative and integral based on the concept of new generalized Caputo-type fractional derivative introduced recently by Odibat and Baleanu (Appl Numer Math 156:94-105, 2020), hence the abbreviated name OBC, in fuzzy environment. Using this concept, we provide some results on the existence and uniqueness of solutions for a class of fractional fuzzy initial value problems of order \(m-1< \kappa < m \) under the newly introduced OBC derivative. Further, we present some applications of the established derivative in the real world with the help of numerical examples based on Euler’s method of integration. Along with a theoretical example, we study an example depicting Allee’s effect and another model of the growth of technological innovations.

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Authors and Affiliations

  1. DST-Centre for Interdisciplinary Mathematical Sciences, Institute of Science, Banaras Hindu University, Varanasi, 221005, India

    Arpit Dwivedi & Ganga Ram Gautam

  2. Department of Mathematics, Swami Devanand P.G. College, Math-Lar, Deoria, 274502, India

    Gunjan Rani

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  1. Arpit Dwivedi
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  2. Gunjan Rani
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  3. Ganga Ram Gautam
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Dwivedi, A., Rani, G. & Gautam, G.R. Analysis on the solution of fractional fuzzy differential equations. Rend. Circ. Mat. Palermo, II. Ser (2024). https://doi.org/10.1007/s12215-024-01006-6

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