The spectral analysis for a singular fractional differential equation with a signed measure

Positive solutions for a system of nonlinear semipositone fractional q q-difference equations with q q-integral boundary conditions

“…In this work we study the following system of nonlinear semipositone fractional q-difference equations with q-integral boundary conditions where α ∈ (2, 3), ν ∈ (1, 2) are real numbers, D α q is the Riemann-Liouville's fractional q-derivative of order α, and the nonnegative constant β, and the functions f i (i = 1, 2) satisfy the conditions (H1) β 0 and 1 − β Recently, there are a large number of papers involving fractional differential equations in the literatures, for example, we refer the readers to [1][2][3][4][5][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] and the references therein. In [7,14] and they obtained the existence of positive solutions by the nonlinear alternative of Leray-Schauder type and the Guo-Krasnosel'skii fixed point theorem.…”

The unique solution of a class of sum mixed monotone operator equations and its application to fractional boundary value problems

“…This is because of both the intensive development of the theory of fractional calculus itself and the wide range of applications of such kind of equations in various scientific fields such as physics, mechanics, chemistry, economics, engineering and biological sciences, etc., see [18,20,21,28]. In recent years, the study of positive solutions for fractional differential equation boundary value problems has attracted considerable attention, and many results have been achieved, and here we refer the reader to [5,6,12,14,15,19,25,29,30,31,32,35,36,37] and the references therein for details.…”

“…These studies not only have theoretical significance but also have a wide range of applications in engineering, nuclear physics, biology, chemistry, technology, etc. Because of the crucial role played by nonlinear equations in applied science as well as mathematics, nonlinear functional analysis has been an active area of research, and nonlinear operators with connection to nonlinear (fractional) differential and integral equations have been extensively studied over the past several decades (see [5,6,12,14,15,19,25,29,30,31,32,35,36,37]). …”

Positive solutions for fractional differential equation involving the Riemann-Stieltjes integral conditions with two parameters

“…Due to the wide application of fractional order differential equations, there are many studies which focus on the solvability of fractional differential equations. For some recent results on this topic, see [1,4,6,7,9,11,12,14,15] and the references therein. El-Shahed [3] considered the following fractional order differential equation…”