  In this paper, we propose new regularization, where integer-order
differential operators are replaced by fractional-order operators.
Regularization for quantum field theories based on application of the Riesz
fractional derivatives of non-integer orders is suggested. The regularized loop
integrals depend on parameter that is the order alpha>0 of the fractional
derivative. The regularization procedure is demonstrated for scalar massless
fields in phi^4-theory on n-dimensional pseudo-Euclidean space-time.
