Journal ArticleDOI
Fuzzy fractional differential equations under generalized fuzzy Caputo derivative
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The related theorems and properties of fuzzy Caputo fractional differential equation FCFDE under the Generalized Hukuhara differentiability are proved in detail and the method is illustrated by solving some examples.Abstract:
In this paper the fuzzy Caputo fractional differential equation FCFDE under the Generalized Hukuhara differentiability is introduced. Also the existence and uniqueness of the solution for a class of fuzzy Caputo fractional differential equation with initial value is studied, and an analytical solution of FCFDE is obtained. The related theorems and properties are proved in detail and the method is illustrated by solving some examples.read more
Citations
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Journal ArticleDOI
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.
Journal ArticleDOI
The solvability of fuzzy fractional partial differential equations under Caputo gH-differentiability
TL;DR: The foundation of the concepts of fuzzy fractional integral and Caputo gH-partial for fuzzy-valued multivariable functions is defined and the appropriateness of local boundary value problems for hyperbolic equations is proved.
Journal ArticleDOI
A note on initial value problems for fractional fuzzy differential equations
TL;DR: In this paper, an appropriate condition is given so that this equivalence between a fractional fuzzy differential equation and a fractionAL fuzzy integral equation are valid.
Journal ArticleDOI
Fuzzy fractional differential equations under Caputo–Katugampola fractional derivative approach
Ngo Van Hoa,Ho Vu,Tran Minh Duc +2 more
TL;DR: An idea of successive approximations under generalized Lipschitz condition is used to prove the existence and uniqueness results of the solution of the initial value problem of Caputo–Katugampola fractional differential equations in fuzzy setting.
References
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Journal ArticleDOI
Analysis of Fractional Differential Equations
Kai Diethelm,Neville J. Ford +1 more
TL;DR: In this paper, the authors discuss existence, uniqueness, and structural stability of solutions of nonlinear differential equations of fractional order, and investigate the dependence of the solution on the order of the differential equation and on the initial condition.
Book
The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type
TL;DR: In this paper, the existence and uniqueness results for Riemann-Liouville Fractional Differential Equations are presented. But they do not cover the special cases of fractional calculus.
Journal ArticleDOI
Fuzzy Random Variables
Madan L. Puri,Dan A. Ralescu +1 more
TL;DR: The new definition of expectation generalizes the integral of a set-valued function and derives the Lebesgue-dominated convergence type theorem by considering a suitable generalization of the Hausdorff metric.
Journal ArticleDOI
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.