Positive Solutions to Toupled System of Fractional Differential Equations

Recently the study of fractional differential equations has attracted the interest of many researcher due to their applications in various fields of sciences and engineering. The applications include viscoelasticity, electrochemistry, control theory and electromagnetism and so on, see for example [1–4]. There are also interesting applications of fractional differential equations to economics, finance and mathematical modeling. For the geometric and physical interpretation of fractional derivatives and integrals, we refer the readers to the book by I. Podlubny [5]. Many authors, [6–11] have studied existence and uniqueness of solutions for fractional differential equations. Nagumotype uniqueness results for fractional differential equations have studied by V. Lakshmikantham and S. Leela [12]. Moreover, existence and multiplicity results for positive solutions to nonlinear fractional differential equations have studied by many researchers, see, [13–15]. The study of coupled fractional differential system has also attracted some attention, see for example, [16–18]. In [19], C. Bai and J. Fang studied existence of positive solution to a coupled system of the type { D 0+u(t) = f(t, v), 0 < t < 1, D 0+v(t) = g(t, u), (1)