On Delta and Nabla Caputo Fractional Differences and Dual Identities

By Thabet Abdeljawad. 2011

174 citations recorded by the source corpus.

We investigate two types of dual identities for Caputo fractional differences. The first type relates nabla and delta type fractional sums and differences. The second type represented by the Q-operator relates left and right fractional sums and differences. Two types of Caputo fractional differences are introduced; one of them (dual one) is defined so that it obeys the investigated dual identities. The relation between Riemann and Caputo fractional differences is investigated, and the delta and nabla discrete Mittag-Leffler functions are confirmed by solving Caputo type linear fractional difference equations. A nabla integration by parts formula is obtained for Caputo fractional differences as well.

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/90e6a712b1fb300ff68aef40caf2daf31da7ac66

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In Applied Mathematics

In Modeling and Simulation

Citations in the corpus

A transference principle for nonlocal operators using a convolutional approach: fractional monotonicity and convexity (2020, background): “In addition, many papers have provided an analysis of various abstract properties of discrete fractional operators—see, for example, the papers by Abdeljawad [5, 6], Anastassiou [9], Atici and Acar [10], Bastos, Mozyrska and Torres [18], Ferreira [23], Lizama [43], Lizama and Murillo-Arcila [45], an”
On fractional derivatives with exponential kernel and their discrete versions (2016, methodology): “The Q−operator action, (Qf)(t) = f(a+ b− t), was used in [20, 23] to relate left and right fractional sums and differences.”