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Han, Bui Thi Ngoc; Linh, Nguyen Thi

The generalized nonlocal boundary condition for fractional Langevin equation with a weakly singular source. (English) Zbl 1518.26006

Rocky Mt. J. Math. 52, No. 6, 1983-2002 (2022).
A class of nonlinear Langevin equations with fractional derivatives of a function depending on another function with generalized nonlocal conditions is investigated. The source function of the problem may have a singularity that appears from the discontinuity of the source function at the initial point. By constructing the formal solution using the Mittag-Lefler function and two parameters and by applying some well-known fixed point theorem, it is proved that the problem has at least one or an unique mild solution. Finally, two examples are given to illustrate the main results.
Reviewer: Xiping Liu (Shanghai)

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:

Langevin equation; fractional derivatives; nonlocal boundary conditions; fixed point theorems
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References:

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