Measure Neutral Functional Differential Equations as Generalized ODEs

  • M. Federson
  • M. Frasson
  • J. G. Mesquita
  • P. H. TacuriEmail author


In this paper, we introduce a class of measure neutral functional differential equations of type
$$\begin{aligned} \mathrm {D}[N(x_t,t)]=f(x_t,t)\mathrm {D}g(t) \end{aligned}$$
through the relation with a certain class of generalized ordinary differential equations introduced in Federson and Schwabik (Differ Integral Equ 19(11):1201–1234, 2006) (we write generalized ODEs), using similar ideas to those of Federson et al. (J Differ Equ 252(6):3816–3847, 2012). By means of the correspondence with generalized ODEs, we state results on the existence, uniqueness and continuous dependences of solutions for our equation of neutral type.


Generalized ordinary differential equations Neutral measure functional differential equations Kurzweil–Henstock–Stieltjes integral 

Mathematics Subject Classification

26A39 34K40 34K05 


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Authors and Affiliations

  1. 1.Instituto de Ciências Matemáticas e de ComputaçãoUniversidade de São PauloSão CarlosBrazil
  2. 2.Instituto de Ciências ExatasUniversidade de BrasiliaBrasíliaBrazil
  3. 3.Faculdade de Ciências e TecnologiaUniversidade Estadual Paulista “Júlio de Mesquita Filho”Presidente PrudenteBrazil

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