Nonholonomic frames for Finsler space with deformed infinite series of (α,β) metric

The purpose of present paper to determine the Finsler spaces due to deformation of special Finsler ( alpha;, beta;) -metric. Consequently, we obtained the non-holonomic frame with the help of alpha;2=aij(x)yiyj, one form metric beta;=bi(x)yi and infinite series of ( alpha;, beta;) metric such as the forms I. ( beta;4 /( beta;- alpha; )2 ) + alpha;2 =F12+F22 i.e. sum of the square of infinite series of ( alpha;, beta;) -metric and square of Riemannian metric II. ( beta;4 /( beta;- alpha; )2 ) + beta;2 =F12+F32 i.e. sum of the square of infinite series of ( alpha;, beta;) -metric and square of 1-form metric.