Ex. 12 



PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 



^/Mj:,«-'^.„*'«,r, ;, = * 



303 



This equation gives u,^, y= -t ^ b 



Ad* — All 



A^x + Ayi 



= Ui -4-Ai 



= (A*, + Ag(i,,,^^-6y) (Ex.11.) 



We have thus succeeded in solving equations with fractional indices of all 

 forms corresponding with the ordinary forms of Linear Differential Equations, 

 whether total or partial, — whether solitary or simultaneous. We have also 

 placed the Calculus of Fractional Differences on the same footing with respect to 

 the ordinary Calculus of Fractional Differences as that which the Calculus of 

 General Differentiation occupies relatively to the ordinary Differential Calculus. 



P. KELLAND. 



Edinbuegh, October 10, 1846. 



