Geodesic
Multiparameter Fractional Differentiation with non singular kernel
Problemy analiza, Tome 10 (2021) no. 3, pp. 15-30

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We introduce here Caputo and Riemann-Liouville type non singular kernel very general multi parameter left and right side fractional derivatives and we prove their continuity. These have the advantage to describe accurately complex situations and phenomena and we can measure their fractional smoothness with memory and nonlocality. Then, we derive related left and right fractional integral inequalities of Hardy, Opial and Hilbert-Pachpatte types, also of Hardy type involving convexity.
Keywords: fractional derivative, multi parameters, fractional integral inequalities.
Mots-clés : Non singular Kernel 
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     author = {George A. Anastassiou},
     title = {Multiparameter {Fractional} {Differentiation} with non singular kernel},
     journal = {Problemy analiza},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2021_10_3_a1/}
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George A. Anastassiou. Multiparameter Fractional Differentiation with non singular kernel. Problemy analiza, Tome 10 (2021) no. 3, pp. 15-30. http://geodesic.mathdoc.fr/item/PA_2021_10_3_a1/