1. bookVolume 79 (2021): Issue 2 (December 2021)
Journal Details
License
Format
Journal
eISSN
1338-9750
First Published
12 Nov 2012
Publication timeframe
3 times per year
Languages
English
access type Open Access

Properties of the Katugampola Fractional Operators

Published Online: 01 Jan 2022
Volume & Issue: Volume 79 (2021) - Issue 2 (December 2021)
Page range: 135 - 148
Received: 21 Oct 2020
Journal Details
License
Format
Journal
eISSN
1338-9750
First Published
12 Nov 2012
Publication timeframe
3 times per year
Languages
English
Abstract

In this work, there are considered higher order fractional operators defined in the sense of Katugampola. There are proved some fundamental properties of the Katugampola fractional operators of any arbitrary real order. Moreover, there are given conditions ensuring existence of the higher order Katugampola fractional derivative in space of the absolutely continuous functions.

Keywords

[1] KATUGAMPOLA, U. N.: New approach to a generalized fractional integral, Appl. Math. Comput. 218 (2011), 860–865. Search in Google Scholar

[2] KATUGAMPOLA, U. N.: A new approach to generalized fractional derivatives, Bull. Math. Anal. App. 6 (2014), 1–15. Search in Google Scholar

[3] AKKURT, A.—KAÇAR, Z.—YILDIRIM, H.: Generalized fractional integral inequalities for continuous random variables, J. Probab. Stat. (2015), Paper no. 958980, 7 pp. Search in Google Scholar

[4] ŁUPlŃSKA, B.—ODZIJEWICZ, T.: A Lyapunov-type inequality with the Katugampola fractional derivative, Math. Methods Appl. Sci.41 (2018), no. 18, 8985–8996. Search in Google Scholar

[5] CHEN, H.—KATUGAMPOLA, U. N.: Hermite-Hadamard and Hermite-Hadamard-Fejér type Inequalities for Generalized Fractional Integrals, J. Math. Anal. Appl. 446 (2017), no. 2, 1274–1291. Search in Google Scholar

[6] ŁUPIŃSKA, B.—ODZIJEWICZ, T.—SCHMEIDEL, E.: On the solutions to a generalized fractional Cauchy problem, Appl. Anal. Discr. Math. 10 (2016), no. 2, 332–344. Search in Google Scholar

[7] ZENG, S.— BALEANU, D.—BAI, Y.—WU, G.: Fractional differential equations of Caputo-Katugampola type and numerical solutions, Appl. Math. Comput. 315 (2017), 549–554. Search in Google Scholar

[8] KATUGAMPOLA,U. N.: Mellin transforms of the generalized fractional integrals and derivatives, Appl. Math. Comput. 257 (2015), 566–580. Search in Google Scholar

[9] CAO, L.—KONG, H.—ZENG, S. D.: Maximum principles for time-fractional Caputo- -Katugampola diffusion equations, J. Nonlinear Sci. Appl. 10 (2017), 2257–2267.10.22436/jnsa.010.04.75 Search in Google Scholar

[10] BALEANU, D.—WU, G. C.—ZENG, S. D.: Chaos analysis and asymptotic stability of generalized Caputo fractional differential equations, Chaos Solitons Fractals 102 (2017), 99–105.10.1016/j.chaos.2017.02.007 Search in Google Scholar

[11] KILBAS, A. A.—SRIVASTAVA, H. M.—TRUJILLO, J. J.: Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006. Search in Google Scholar

[12] KILBAS, A. A.: Hadamard-type fractional calculus, J. Korean Math. Soc. 38(6) (2001), 1191–1204. Search in Google Scholar

[13] COTTONE, G.—MALINOWSKA, A. B.—ODZIJEWICZ, T.: The non-homogeneous Voigt-Katugampola model of visco-elastic material (to appear) Search in Google Scholar

[14] ŁUPIŃSKA, B.—ODZIJEWICZ, T.—SCHMEIDEL, E.: Some properties of generalized fractional integrals and derivatives, In: Proceedings of the International Conference of Numerical Analysis and Applied Mathematics 2016 (ICNAAM-2016) Book Series: AIP Conference Proceedings.10.1063/1.4992317 Search in Google Scholar

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