Generalized Taylor’s formula

Abstract: In this paper, a new generalized Taylor’s formula of the kindwhere a j ∈ R , x > a, 0< α ⩽1, is established. Such an expression is precisely the classical Taylor’s formula in case of α =1. In addition, detailed expressions for and a j (α), that involving Caputo fractional derivatives, are well constructed. Some applications including approximation of functions and solutions of fractional differential equations are also given. [Copyright &y& Elsevier]