On Hilfer fractional difference operator

[摘要] In this article, a new definition of fractional Hilfer difference operator is introduced. Definition based properties are developed and utilized to construct fixed point operator for fractional order Hilfer difference equations with initial condition. We acquire some conditions for existence, uniqueness, Ulam–Hyers, and Ulam–Hyers–Rassias stability. Modified Gronwall’s inequality is presented for discrete calculus with the delta difference operator.

[学科分类] 航空航天科学

[关键词] Hilfer fractional difference;Discrete Mittag-Leffler functions;Delta Laplace transform;Gronwall’s inequality;Existence and uniqueness;Ulam stability of initial value problem