The $m-$extension of Fibonacci and Lucas $p-$difference sequences

Abstract

In this paper we define the $m-$extension of Fibonacci and Lucas $p-$difference sequence by using the $m-$extension of Fibonacci and Lucas $p-$numbers. We investigate some properties of our new sequence and introduce some relations between the $m-$extension of Fibonacci and Lucas $p-$difference sequence and the $m-$extension of Fibonacci and Lucas $p-$numbers. Moreover,  we present the sums and generating function of the $m-$extension of Fibonacci and Lucas $p-$difference sequence. Finally, we study the $m-$extension of Fibonacci $p-$difference Newton polynomial interpolation.