scholarly journals Results on initial value problems for random fuzzy fractional functional differential equations

Filomat ◽  
2018 ◽  
Vol 32 (7) ◽  
pp. 2601-2624
Author(s):  
Ho Vu ◽  
Ngo Hoa ◽  
Nguyen Son ◽  
Donal O’Regane
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Euler Method ◽  
Successive Approximations ◽  
Initial Value ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Functional Differential ◽  
Fractional Functional Differential Equations ◽  
Fractional Functional

In this paper random fuzzy fractional functional differential equations (RFFFDEs) with Caputo generalized Hukuhara differentiability are introduced. We present existence and uniqueness results for RFFFDEs using the idea of successive approximations. The behaviour of solutions when the data of the equation are subjected to errors is discussed. Furthermore, the solution to random fuzzy fractional functional initial value problem under Caputo-type fuzzy fractional derivatives by a modified fractional Euler method (MFEM) is presented. The results are illustrated with examples.

scholarly journals Uniform Asymptotic Stability of Solutions of Fractional Functional Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Yajing Li ◽  
Yejuan Wang
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Functional Differential Equations ◽  
Stability Of Solutions ◽  
Uniform Asymptotic Stability ◽  
Initial Value ◽  
Functional Differential ◽  
Fractional Functional Differential Equations ◽  
Stability Results ◽  
Fractional Functional

Some global existence and uniform asymptotic stability results for fractional functional differential equations are proved. It is worth mentioning that whenα=1the initial value problemDαyteβt=ft,yteβt,  t∈t0,∞,  t0⩾0,  0<α<1,  yt=ϕt,  t0-h⩽t⩽t0,reduces to a classical dissipative differential equation with delays as in Caraballo et al.'s work (2005).

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