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of 30
pro vyhledávání: '"26A33, 26E70"'
In this paper, we investigate the existence of the asymptotically almost automorphic solution of the following type of abstract nonlinear integro-dynamic equation \begin{eqnarray*} y^{\Delta}(s) &=&Ay(s)+\mathcal{F}\left(s,y(s),\int\limits_{t_0}^{s}{
Externí odkaz:
http://arxiv.org/abs/2404.11616
Publikováno v:
Math. Meth. Appl. Sci. 46 (2023), no. 12, 12378--12401
We introduce a new version of $\psi$-Hilfer fractional derivative, on an arbitrary time scale. The fundamental properties of the new operator are investigated and, in particular, we prove an integration by parts formula. Using the Laplace transform a
Externí odkaz:
http://arxiv.org/abs/2302.12183
In this manuscript we investigate the existence and uniqueness of an impulsive fractional dynamic equation on time scales involving non-local initial condition with help of Caputo nabla derivative. The existency is based on the Scheafer's fixed point
Externí odkaz:
http://arxiv.org/abs/2207.01517
Publikováno v:
Axioms 10 (2021), no. 4, Art. 317, 15 pp
In this paper, we introduce the nabla fractional derivative and fractional integral on time scales in the Riemann-Liouville sense. We also introduce the nabla fractional derivative in Gr\"unwald-Letnikov sense. Some of the basic properties and theore
Externí odkaz:
http://arxiv.org/abs/2112.13083
Autor:
Torres, Delfim F. M.
Publikováno v:
Appl. Math. Lett. 121 (2021), Art. 107407, 6 pp
We prove Cauchy's formula for repeated integration on time scales. The obtained relation gives rise to new notions of fractional integration and differentiation on arbitrary nonempty closed sets.
Comment: This is a preprint of a paper whose fina
Comment: This is a preprint of a paper whose fina
Externí odkaz:
http://arxiv.org/abs/2105.04921
Publikováno v:
Nonlinear Anal. Hybrid Syst. 32 (2019), 168--176
Caputo-Fabrizio fractional delta derivatives on an arbitrary time scale are presented. When the time scale is chosen to be the set of real numbers, then the Caputo-Fabrizio fractional derivative is recovered. For isolated or partly continuous and par
Externí odkaz:
http://arxiv.org/abs/1812.00266
Publikováno v:
Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 68 (2019), no. 1, 1186--1196
We introduce the notion of structural derivative on time scales. The new operator of differentiation unifies the concepts of fractal and fractional order derivative and is motivated by lack of classical differentiability of some self-similar function
Externí odkaz:
http://arxiv.org/abs/1811.09474
Publikováno v:
Studies in Systems, Decision and Control 194 (2019), 35--47
We introduce new fractional operators of variable order on isolated time scales with Mittag-Leffler kernels. This allows a general formulation of a class of fractional variational problems involving variable-order difference operators. Main results g
Externí odkaz:
http://arxiv.org/abs/1809.02029
We survey methods and results of fractional differential equations in which an unknown function is under the operation of integration and/or differentiation of fractional order. As an illustrative example, we review results on fractional integral and
Externí odkaz:
http://arxiv.org/abs/1807.01529
Publikováno v:
J. King Saud Univ. Sci. 30 (2018), no. 3, 381--385
Using a fixed point theorem in a proper Banach space, we prove existence and uniqueness results of positive solutions for a fractional Riemann-Liouville nonlocal thermistor problem on arbitrary nonempty closed subsets of the real numbers.
Commen
Commen
Externí odkaz:
http://arxiv.org/abs/1703.05439