PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 308 
Z 7 
Bx 12: A,” Un, y— 4? Uy, y= 
Thi ae 1 
1S equation QIVES Uz, y= 
q 5 yl Bn? — Ay? 
Ate + Ay b 
~ A,—A 

=(a?, +4#,) (Py 40—5Y) (Ex. Ln) 
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. 
EprinsureH, October 10, 1846. 

