English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

In this paper, we deal with a Cauchy problem for a nonlinear fractionaldifferential equation with the Caputo derivative of order $\alpha \in (0, 1)$.As initial data, we consider a pair consisting of an initial point, which doesnot necessarily coincide with the inferior limit of the fractional derivative,and a function that determines the values of a solution on the interval fromthis inferior limit to the initial point. We study differentiability propertiesof the functional associating initial data with the endpoint of thecorresponding solution of the Cauchy problem. Stimulated by recent results onthe dynamic programming principle and Hamilton--Jacobi--Bellman equations forfractional optimal control problems, we examine so-called fractionalcoinvariant derivatives of order $\alpha$ of this functional. We prove thatthese derivatives exist and give formulas for their calculation.

On differentiability of solutions of fractional differential equations with respect to initial data