\(k\)-fractional integrals and application. (English) Zbl 1248.33005
Summary: The purpose is to introduce a variant of fractional integrals to be called \(k\)-fractional integrals which are based on the \(k\)-gamma function. When \(k \rightarrow 1\), it turns out to be the usual Riemann-Liouville fractional integral. The use of \(k\)-fractional integrals is also illustrated.
MSC:
33B15 | Gamma, beta and polygamma functions |
33D05 | \(q\)-gamma functions, \(q\)-beta functions and integrals |
26A33 | Fractional derivatives and integrals |