Journal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Volume 60, Issue -, Pages 72-91Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cnsns.2018.01.005
Keywords
Fractional calculus; Psi-Hilfer fractional derivative; A class of fractional derivatives and integrals
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In this paper we introduce a new fractional derivative with respect to another function the so-called Psi-Hilfer fractional derivative. We discuss some properties and important results of the fractional calculus. In this sense, we present some results involving uniformly convergent sequence of function, uniformly continuous function and examples including the Mittag-Leffler function with one parameter. Finally, we present a wide class of integrals and fractional derivatives, by means of the fractional integral with respect to another function and the Psi-Hilfer fractional derivative. (C) 2018 Elsevier B.V. All rights reserved.
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