Dear M. P. Chaudhary,

There exist numerous definitions of hypergeometric functions. They constitute a wide class of special functions. All of them satisfy differential equations of some sort. Could you please be more precise and tell what functions you would like to have equations for? What is the precise definition for the H-function that you are using?

Differential equations for hypergeometric functions is one of the central topics in my book on hypergeometric and algebraic functions in several complex variables, see my homepage at ResearchGate. 

Sincerely,

Timur Sadykov.

tray to eliminate constants by differentiating given function  either hyp geo or h-function and get corresponding differential equation is usual method

I think the easiest and best way is using operational methods , see papers of professor G Dattoli

https://www.researchgate.net/profile/Giuseppe_Dattoli2

sorry for late answer