N-Dimensional Fractional Lagrange’s Inversion Theorem
نویسندگان
چکیده
and Applied Analysis 3 Theorem8. Let (α ≥ 0) ∈ R.Then, for everyf(x) ∈ L 1 [a, b], Dα a Jα a f(x) = f(x). Proof. For α = 0, both operator, are the identity. For α > 0, letm ≥ ⌈α⌉; then, D α a J α a f (x) = D m a J m−α a J α a f (x) = D m a J m a f (x) = D m a J m a f(x) = f(x) . (7) Corollary 9. Letf be analytic in (a−h, a+h) for some h > 0, and let (α ≥ 0) ∈ R. Then, (I-1) Jα a f(x) = ∞
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