On generalized fractional operators and a gronwall type inequality with applications
By Y. Adjabi, Fahd Jarad, Thabet Abdeljawad. 2017
59 citations recorded by the source corpus.
In this paper, we obtain the Gronwall type inequality for generalized fractional operators unifying Riemann-Liouville and Hadamard fractional operators. We apply this inequality to the dependence of the solution of differential equations, involving generalized fractional derivatives, on both the order and the initial conditions. More properties for the generalized fractional operators are formulated and the solutions of initial value problems in certain new weighted spaces of functions are established as well.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/ad7cf76b637d4205d2dbba7aa0e8afea1f6d87cd
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In Applied Mathematics
- Fahd Jarad
- Thabet Abdeljawad
- Dumitru Băleanu
- Mehmet Yavuz
- Arran Fernandez
- Y. Chu
- Guo-cheng Wu
- Saima Rashid
Citations in the corpus
- Generalized fractional derivatives and Laplace transform (2020, background): “Applications on such derivatives can be seen in [10, 11, 1, 2, 5, 6] and the references therein.”
- Existence and uniqueness of solutions to fractional differential equations in the frame of generalized Caputo fractional derivatives (2018, unknown): “7 ([27]) Let 0 < a < b < ∞, α > 0, and 0 ≤ < 1, then (a) If 0 < α < , then aI is bounded from C ,ρ[a, b] into C –α,ρ[a, b]: ∥∥ aI α,ρ f ∥∥ C –α,ρ ≤ ( b – a ρ )α (1 – ) (1 + α – ) ‖f ‖C ,ρ ; (41)”