@article{Potapov2025, 
author = {Alexander A. Potapov and Vetlugin D. Beybalaev and Abutrab A. Aliverdiev},
title = {On a boundary value problem for a nonlinear differential equation with a Riemann-Liouville fractional derivative of variable order and nonlocal boundary conditions},
year = {2025},
journal = {Electronic Research Archive},
volume = {33},
number = {9},
pages = {5829-5844},
keywords = {fractional derivative, boundary conditions, Green function, non-stationary processes},
url = {https://www.sciopen.com/article/10.3934/era.2025259},
doi = {10.3934/era.2025259},
abstract = {The paper studies the existence of at least two positive solutions for a nonlinear differential equation with a fractional Riemann-Liouville derivative of variable order and nonlocal boundary conditions. To transform the original equation into an integral equation, the Green function is constructed and boundedness conditions for the Green function are obtained. A theorem on the existence of at least two positive solutions to the problem is proven. An example is given that shows the existence of two positive solutions, and approximation graphs are constructed for clarity.}
}