\((k,\psi)\)-Hilfer variational problem. (English) Zbl 1515.26014
Summary: In this paper, we study variational structure for the \((k,\psi )\)-Hilfer fractional derivative operator. We investigate some properties of \((k,\psi )\)-Hilfer fractional integral and derivative which are used of variational structure. Also, using variational methods and critical point theory, we study the existence of solutions to a problem with \((k,\psi )\)-Hilfer fractional derivative. Our work extent and improve some recent works in the literature.
MSC:
| 26A33 | Fractional derivatives and integrals |
| 34A08 | Fractional ordinary differential equations |
| 34A12 | Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations |
Keywords:
\((k, \psi)\)-fractional operators; fractional integration by parts; fractional space; variational methodsReferences:
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