Journal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Volume 77, Issue -, Pages 305-311Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cnsns.2019.05.003
Keywords
psi-Hilfer fractional operator; Leibniz type rule; Leibniz rule
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Funding
- PNPD-CAPES scholarship of the Postgraduate Program in Applied Mathematics of IMECC-Unicamp
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In this paper, we present a Leibniz type rule for the psi-Hilfer (psi-H) fractional derivative operator in two forms, one written in terms of the psi-Riemann-Liouville (psi-RL) fractional derivative operator and the other in terms of the psi-H fractional derivative operator. Direct consequences of this new formulation of a Leibniz type rule are the possibility of writing recurrence relations involving solutions of fractional differential equations and of investigating the existence, uniqueness and Ulam-Hyers stabilities of mild solutions of fractional differential equations involving psi-H fractional operator. We present some specific cases of Leibniz type rule for the psi-H fractional derivative operator which emerge from different choices of parameter beta and the function psi. (C) 2019 Elsevier B.V. All rights reserved.
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