Sajjadmanesh, MojtabaBaleanu, DumitruAfshari, Hojjat2021-01-292025-09-182021-01-292025-09-182020Afshari, Hojjat; Sajjadmanesh, Mojtaba; Baleanu, Dumitru (2020). "Existence and uniqueness of positive solutions for a new class of coupled system via fractional derivatives", Advances in Difference Equations, Vol. 2020, No. 1.1687-1847https://doi.org/10.1186/s13662-020-02568-2https://hdl.handle.net/20.500.12416/12331Afshari, Hojat/0000-0003-1149-4336In this paper we study the existence of unique positive solutions for the following coupled system: {Da0 + x(t) + f1(t, x(t), D. 0+ x(t)) + g1(t, y(t)) = 0, D beta 0+ y(t) + f2(t, y(t), D. 0+ y(t)) + g2(t, x(t)) = 0, t. (0, 1), n - 1 < a, beta < n; x(i)(0) = y(i)(0) = 0, i = 0, 1, 2,..., n - 2; [D. 0+ y(t)] t=1 = k1(y(1)), [D. 0+ x(t)] t=1 = k2(x(1)), where the integer number n > 3 and 1 =. =. = n - 2, 1 =. =. = n - 2, f1, f2 : [0, 1] xR+ xR+. R+, g1, g2 : [0, 1] xR+. R+ and k1, k2 : R+. R+ are continuous functions, Da0 + and D beta 0+ stand for the Riemann-Liouville derivatives. An illustrative example is given to show the effectiveness of theoretical results.eninfo:eu-repo/semantics/openAccessFractional Differential EquationMixed Monotone OperatorNormal ConeCoupled SystemArticle10.1186/s13662-020-02568-22-s2.0-85081718884