Type-2 fuzzy fractional derivatives |
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| Institution: | 1. Department of Physics, Chemistry and Mathematics, Federal University of São Carlos, Sorocaba, SP, Brazil;2. Department of Applied Mathematics, IMECC, University of Campinas, Campinas, SP, Brazil;1. Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran;2. Department of Electrical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran;1. Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran;2. Department of Mathematics and Computer, Izmir University, Izmir, Turkey;1. Department of Electrical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran;2. Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran |
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| Abstract: | In this paper, we introduce two definitions of the differentiability of type-2 fuzzy number-valued functions of fractional order. The definitions are in the sense of Riemann–Liouville and Caputo derivative of order β ? (0, 1), and based on type-2 Hukuhara difference and H2-differentiability. The existence and uniqueness of the solutions of type-2 fuzzy fractional differential equations (T2FFDEs) under Caputo type-2 fuzzy fractional derivative and the definition of Laplace transform of type-2 fuzzy number-valued functions are also given. Moreover, the approximate solution to T2FFDE by a Predictor-Evaluate–Corrector-Evaluate (PECE) method is presented. Finally, the approximate solutions of two examples of linear and nonlinear T2FFDEs are obtained using the PECE method, and some cases of T2FFDEs applications in some sciences are presented. |
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| Keywords: | Type-2 fuzzy sets Type-2 Hukuhara difference Type-2 fuzzy fractional differential equations Caputo type-2 fuzzy fractional derivative Riemann–Liouville type-2 fuzzy fractional derivative |
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