RT Journal Article
T1 Fractional Langevin Equation Involving Two Fractional Orders: Existence and Uniqueness Revisited
A1 Fazli, Hossein
A1 Sun, HongGuang
A1 Nieto Roig, Juan José
K1 Fractional Langevin equation
K1 Mittag–Leffler function
K1 Prabhakar integral operator
K1 Existence
K1 Uniqueness
AB We consider the nonlinear fractional Langevin equation involving two fractional orders with initial conditions. Using some basic properties of Prabhakar integral operator, we find an equivalent Volterra integral equation with two parameter Mittag–Leffler function in the kernel to the mentioned equation. We used the contraction mapping theorem and Weissinger’s fixed point theorem to obtain existence and uniqueness of global solution in the spaces of Lebesgue integrable functions. The new representation formula of the general solution helps us to find the fixed point problem associated with the fractional Langevin equation which its contractivity constant is independent of the friction coefficient. Two examples are discussed to illustrate the feasibility of the main theorems
PB MDPI
YR 2020
FD 2020
LK http://hdl.handle.net/10347/23641
UL http://hdl.handle.net/10347/23641
LA eng
NO Fazli, H.; Sun, H.; Nieto, J.J. Fractional Langevin Equation Involving Two Fractional Orders: Existence and Uniqueness Revisited. Mathematics 2020, 8, 743
NO The authors are thankful to the Editor(s) and reviewers of the manuscript for their helpful comments. The work of H. Fazli and H. Sun was supported by the National Key R&D Program of China (2017YFC0405203), the National Natural Science Foundation of China under Grant No. 11972148. The reserach of J. J. Nieto was partially supported by Xunta de Galicia, ED431C 2019/02, and by project MTM2016-75140-P of AEI/FEDER (Spain)
DS Minerva
RD 24 abr 2026