In: Mathematica Slovaca, vol. 68, no. 6
Rok, strany: 2018, 1353 - 1366
fractional Hadamard-type derivatives and integrals, weighted spaces of summable and absolutely continuous functions, fractional Cauchy problem, Banach contraction principle
In this paper, we investigate some Cauchy problems involving a left-sided Hadamard-type fractional derivative. A theorem on the existence of a unique solution to a nonlinear problem is proved. The main result is obtained using a fixed point theorem due to Banach, as well as the Bielecki norm. A Cauchy formula for the solution of the linear problem is derived.
Kamocki, R. 2018. Cauchy problems involving a Hadamard-type fractional derivative. In Mathematica Slovaca, vol. 68, no.6, pp. 1353-1366. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0186
Kamocki, R. (2018). Cauchy problems involving a Hadamard-type fractional derivative. Mathematica Slovaca, 68(6), 1353-1366. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0186
Publikované: 3. 12. 2018