Laadjal, ZaidJarad, FahdJarad, FahdMatematik2022-10-042022-10-042022Laadjal, Zaid; Jarad, Fahd (2022). "On a langevin equation involving caputo fractional proportional derivatives with respect to another function", AIMS Mathematics, Vol. 7, No. 1, pp. 1273-1292.2473-6988https://doi.org/10.3934/math.2022075Laadjal, Zaid/0000-0003-1627-2898In this work, we introduce and study a class of Langevin equation with nonlocal boundary conditions governed by a Caputo fractional order proportional derivatives of an unknown function with respect to another function. The qualitative results concerning the given problem are obtained with the aid of the lower regularized incomplete Gamma function and applying the standard fixed point theorems. In order to homologate the theoretical results we obtained, we present two examples.eninfo:eu-repo/semantics/openAccessCaputo Fractional Proportional Order Derivative With Respect To Another FunctionLangevin EquationIncomplete Gamma FunctionFixed Point TheoremsArticle711273129210.3934/math.20220752-s2.0-85117610986WOS:000718878200066Q1Q1