Abstract
By using the method of reducing the order of a derivative, the higher-order fractional differential equation is transformed into the lower-order fractional differential equation and combined with the mixed monotone operator, a unique positive solution is obtained in this paper for a singular p-Laplacian boundary value system with the Riemann–Stieltjes integral boundary conditions. This equation system is very wide because there are many parameters, which can be changeable in the equation system in this paper, and the nonlinearity is allowed to be singular in regard to not only the time variable but also the space variable. Moreover, the unique positive solution that we obtained in this paper is dependent on λ, and an iterative sequence and convergence rate are given, which are important for practical application. An example is given to demonstrate the application of our main results.
Highlights
During the last decades, boundary value problems for nonlinear fractional differential equations have gained its popularity and significance due to its distinguished applications c Vilnius University, 2018 as valuable tools in different areas of applied different areas such as physics, chemistry, electrical networks, economics, rheology, biology chemical, image processing, and so on
Fractional calculus have been shown to be more accurate and realistic than integerorder models, and it provides an excellent tool to describe the hereditary properties of material and processes, in viscoelasticity, electrochemistry, porous media, and so on
There has been a significant development in the study of fractional differential equations in recent years
Summary
Boundary value problems for nonlinear fractional differential equations have gained its popularity and significance due to its distinguished applications. 1 0 v(s) dB(s) denote the Riemann–Stieltjes integrals of u, v with respect to A and B, respectively, A, B are bounded variations, f : (0, 1) × R3+ → R, g : (0, 1) × R+ → R are two continuous functions and may be singular at t = 0, 1, Dtα, Dtβ, Dtγ are the standard Riemann–Liouville derivatives. Motivated by the excellent results above, in this paper, we will devote to considering the following singular p-Laplacian fractional differential equation (PFDE) with the Riemann–Stieltjes integral boundary conditions: D0α+ φp D0γ+u (t) + λ1/(q−1)f t, u(t), D0μ+1 u(t), D0μ+2 u(t), .
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
