On a Caputo-type fractional derivative
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Daniela S. Oliveira
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Edmundo Capelas de Oliveira
Abstract
In this paper, we present a new differential operator of arbitrary order defined by means of a Caputo-type modification of the generalized fractional derivative recently proposed by Katugampola. The generalized fractional derivative, when convenient limits are considered, recovers the Riemann–Liouville and the Hadamard derivatives of arbitrary order. Our differential operator recovers as limiting cases the arbitrary order derivatives proposed by Caputo and by Caputo–Hadamard. Some properties are presented as well as the relation between this differential operator of arbitrary order and the Katugampola generalized fractional operator. As an application we prove the fundamental theorem of fractional calculus associated with our operator.
Acknowledgements
We are indebted to Dr. J. Emílio Maiorino for useful and fruitful discussions. We are grateful to the referees for the suggestions which have helped make this work clearer.
References
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© 2019 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- On a Caputo-type fractional derivative
- Well-posedness, blow-up dynamics and controllability of the classical chemotaxis model
- Sine and cosine type functional equations on hypergroups
- Solvability of positive solutions for a systems of nonlinear fractional order BVPs with p-Laplacian
- On commutativity of rings and Banach algebras with generalized derivations
- Extension of Zelazko’s theorem to n-Jordan homomorphisms
- Asymptotic behavior of the Timoshenko-type system with nonlinear boundary control
Artikel in diesem Heft
- Frontmatter
- On a Caputo-type fractional derivative
- Well-posedness, blow-up dynamics and controllability of the classical chemotaxis model
- Sine and cosine type functional equations on hypergroups
- Solvability of positive solutions for a systems of nonlinear fractional order BVPs with p-Laplacian
- On commutativity of rings and Banach algebras with generalized derivations
- Extension of Zelazko’s theorem to n-Jordan homomorphisms
- Asymptotic behavior of the Timoshenko-type system with nonlinear boundary control
