Bai, Chuan-zhi; Fang, Jin-xuan The existence of a positive solution for a singular coupled system of nonlinear fractional differential equations. (English) Zbl 1061.34001 Appl. Math. Comput. 150, No. 3, 611-621 (2004). The authors discuss the existence of a positive solution to the singular coupled system \[ D^s u= f(t,v), \quad D^pv= g(t, u),\quad 0< t< 1,\tag{1} \] where \(0< s< 1\), \(0< p< 1\), \(D^s\) and \(D^p\) are two standard Riemann-Liouville fractional derivatives, \(f,g: (0,1]\times [0,+\infty)\to [0,+\infty)\) are two given continuous functions. The proof of the existence result for (1) is based on some kind of fixed-point theorem in cones. Reviewer: Messoud A. Efendiev (Berlin) Cited in 116 Documents MSC: 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations 26A33 Fractional derivatives and integrals Keywords:singular nonlinear fractional differential equation; positive solution; fixed-point theorem in cones PDF BibTeX XML Cite \textit{C.-z. Bai} and \textit{J.-x. Fang}, Appl. Math. Comput. 150, No. 3, 611--621 (2004; Zbl 1061.34001) Full Text: DOI OpenURL References: [1] Campos, L.M.C.M., On the solution of some simple fractional differential equations, Int. J. math. sci., 13, 481-496, (1990) · Zbl 0711.34019 [2] Delbosco, D.; Rodino, L., Existence and uniqueness for a nonlinear fractional differential equation, J. math. anal. appl., 204, 609-625, (1996) · Zbl 0881.34005 [3] Granas, A.; Guenther, R.B.; Lee, J.W., Some general existence principle in the Carathéodory theory of nonlinear systems, J. math. pures appl., 70, 153-196, (1991) · Zbl 0687.34009 [4] Kilbas, A.A.; Trujillo, J.J., Differential equations of fractional order: methods, results, and problems. I, Appl. anal., 78, 153-192, (2001) · Zbl 1031.34002 [5] Krasnoselskii, M.A., Positive solutions of operator equations, (1964), Noordhoff Groningen [6] Ling, Y.; Ding, S., A class of analytic functions defined by fractional derivative, J. math. anal. appl., 186, 504-513, (1994) · Zbl 0813.30016 [7] Miller, K.S.; Ross, B., An introduction to the fractional calculus and fractional differential equation, (1993), Wiley New York · Zbl 0789.26002 [8] Samko, S.G.; Kilbas, A.A.; Marichev, O.I., Fractional integrals and derivatives. theory and applications, (1993), Gordon and Breach · Zbl 0818.26003 [9] Zhang, S., The existence of a positive solution for a nonlinear fractional differential equation, J. math. anal. appl., 252, 804-812, (2000) · Zbl 0972.34004 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.