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Received March 4, 2020; Accepted May 30, 2020; Published June 14, 2020.
Abstract. In this paper, we study the Langevin equation within the generalized proportional fractional derivative. The proposed equation involves a variable coefficient and subjects to mixed integro-differential boundary conditions. We introduce the generalized proportional fractional derivative and expose some of its features. We mainly investigate the existence, uniqueness and different types of Ulam stability of the solutions via fixed point theorems and inequality techniques. Finally, we provide two examples to support our main results.
How to Cite this Article:
Weerawat Sudsutad, Jehad Alzabut, Somsiri Nontasawatsri, Chatthai Thaiprayoon, Stability analysis for a generalized proportional fractional Langevin equation with variable coefficient and mixed integro-differential boundary conditions, Journal of Nonlinear Functional Analysis, Vol. 2020 (2020), Article ID 23, pp. 1-24.