Journal ArticleDOI
Global solutions for nonlinear fuzzy fractional integral and integrodifferential equations
Robab Alikhani,Fariba Bahrami +1 more
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In this article, the authors considered the existence and uniqueness results for fuzzy fractional integral equations employing the method of upper and lower solutions and proved the existence of solutions for the fuzzy initial value problem of fractional integrodifferential equations involving Riemann-Liouville differential operators.About:
This article is published in Communications in Nonlinear Science and Numerical Simulation.The article was published on 2013-08-01. It has received 53 citations till now. The article focuses on the topics: Initial value problem & Nonlinear system.read more
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On Analytical Solutions of the Fractional Differential Equation with Uncertainty: Application to the Basset Problem
TL;DR: This paper applies Caputo’s H-differentiability, constructed based on the generalized Hukuhara difference, to solve the fuzzy fractional differential equation (FFDE) with uncertainty, and introduces the fuzzy Laplace transform of the Caputo H-derivative.
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Fuzzy fractional functional differential equations under Caputo gH-differentiability
TL;DR: The existence and uniqueness results of solutions for FFFDEs under Caputo generalized Hukuhara differentiability are studied and the solution to fuzzy fractional functional initial value problem by a modified Adams–Bashforth–Moulton method is presented.
Journal ArticleDOI
Fuzzy fractional functional integral and differential equations
TL;DR: In this article, the existence and uniqueness results for fuzzy fractional functional integral equations employing the contraction principle were derived for the functional initial value problem under Caputo-type fuzzy fractions derivatives by a modified fractional Euler method.
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Uncertain viscoelastic models with fractional order: a new spectral tau method to study the numerical simulations of the solution
TL;DR: A new model based on fractional calculus is proposed to deal with the Kelvin–Voigt (KV) equation and non-Newtonian fluid behavior model with fuzzy parameters and a new and accurate numerical algorithm based on the generalized fractional Legendre polynomials (GFLPs) is developed to solve those problems under uncertainty.
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Fractional Order Sallen---Key and KHN Filters: Stability and Poles Allocation
TL;DR: The analysis for allocating the system poles and hence controlling the system stability for KHN and Sallen–Key fractional order filters and the effect of the transfer function parameters on the singularities of the system is demonstrated.
References
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Book
Theory and Applications of Fractional Differential Equations
TL;DR: In this article, the authors present a method for solving Fractional Differential Equations (DFE) using Integral Transform Methods for Explicit Solutions to FractionAL Differentially Equations.
Journal ArticleDOI
Elementary fuzzy calculus
Roy H. Goetschel,William Voxman +1 more
TL;DR: This paper shall view fuzzy numbers in a topological vector space setting using the customary vector space operations together with the metric given in [4] to define differentiation and integration of fuzzy-valued functions in ways that parallel closely the corresponding definitions for real differentiation and Integration.
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Differentials of fuzzy functions
Madan L. Puri,Dan A. Ralescu +1 more
TL;DR: The Radstrom embedding theorem is generalized and is used to define the concept of the differential of a fuzzy function.
Journal ArticleDOI
Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations
Barnabás Bede,Sorin G. Gal +1 more
TL;DR: generalized concepts of differentiability (of any order n@?N), which solves this shortcoming of fuzzy number differentiability, are introduced and some concrete applications to partial and ordinary fuzzy differential equations with fuzzy input data of the form c@?g(x).
Posted Content
Geometric and Physical Interpretation of Fractional Integration and Fractional Differentiation
Igor Podlubny,B. Nemcovej +1 more
TL;DR: In this paper, a solution to the more than 300-year old problem of geometric and physical interpretation of fractional integration and dieren tiation is suggested for the Riemann-Liouville fractional Integration and Dieren Tiation, the Caputo fractional dierentiation, and the Riesz potential.