Arbitrary Order Fractional Difference Operators with Discrete Exponential Kernels and Applications
By Thabet Abdeljawad, Q. Al‐Mdallal, Mohamed Ali Hajji. 2017
57 citations recorded by the source corpus.
Recently, Abdeljawad and Baleanu have formulated and studied the discrete versions of the fractional operators of order with exponential kernels initiated by Caputo-Fabrizio. In this paper, we extend the order of such fractional difference operators to arbitrary positive order. The extension is given to both left and right fractional differences and sums. Then, existence and uniqueness theorems for the Caputo ( ) and Riemann ( ) type initial difference value problems by using Banach contraction theorem are proved. Finally, a Lyapunov type inequality for the Riemann type fractional difference boundary value problems of order is proved and the ordinary difference Lyapunov inequality then follows as tends to from right. Illustrative examples are discussed and an application about Sturm-Liouville eigenvalue problem in the sense of this new fractional difference calculus is given.
Subfields: Applied Mathematics, Modeling and Simulation
View Paper: https://www.semanticscholar.org/paper/02cb4ee5f280e418b36939f854d407a8834d72e3
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In Applied Mathematics
- Fahd Jarad
- Thabet Abdeljawad
- Y. Adjabi
- Dumitru Băleanu
- Mehmet Yavuz
- Arran Fernandez
- Y. Chu
- Guo-cheng Wu
In Modeling and Simulation
- Fahd Jarad
- Thabet Abdeljawad
- Y. Adjabi
- Dumitru Băleanu
- Arran Fernandez
- Mehmet Yavuz
- Chokkalingam Ravichandran
- Hafiz Muhammad Fahad
Citations in the corpus
- On generalized fractional operators and a gronwall type inequality with applications (2017, methodology): “Other types of inequalities were considered in [20, 21] In this paper, we generalize the Gronwall inequality to differential equations involving a two-parameter generalized fractional derivative [22, 23] which provides the Riemann-Liouville and Hadamard fractional derivatives when one of the paramet”