6533b871fe1ef96bd12d10ab

RESEARCH PRODUCT

Maximal ℓ p ‐regularity of multiterm fractional equations with delay

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[EN] We provide a characterization for the existence and uniqueness of solutions in the space of vector-valued sequences l(p) (Z, X)for the multiterm fractional delayed model in the form Delta(alpha)u(n) + lambda Delta(beta)u(n) = Lambda u(n) + u(n-tau) + f(n), n is an element of Z, alpha, beta is an element of R+, tau is an element of Z, lambda is an element of R, where X is a Banach space, A is a closed linear operator with domain D(A) defined on X, f is an element of l(p)(Z,X) and Delta(Gamma) denotes the Grunwald-Letkinov fractional derivative of order Gamma > 0. We also give some conditions to ensure the existence of solutions when adding nonlinearities. Finally, we illustrate our results with an example given by a general abstract nonlinear model that includes the fractional Fisher equation with delay.