Variational Methods for an Impulsive Fractional Differential Equations with Derivative Term

Abstract

This paper is devoted to studying the existence of solutions to a class of impulsive fractional differential equations with derivative dependence. The used technical approach is based on variational methods and iterative methods. In addition, an example is given to demonstrate the main results.

Explicit monotone iterative sequences for positive solutions of a fractional differential system with coupled integral boundary conditions on a half-line

“…Fractional-order differential equations is a natural generalization of the case of integer order, which has become the focus of attention involving various kinds of boundary conditions because of the wide application in mathematical models and applied sciences. Some latest results on the topic can be found in a series of papers [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] and the references therein. In particular, a monotone iterative technique is believed to be an efficient and important method to deal with sequences of monotone solutions for initial and boundary value problems.…”

Monotone iterative schemes for positive solutions of a fractional differential system with integral boundary conditions on an infinite interval

“…In recent decades, there has been a rapid growth in the number of fractional calculus from both theoretical and applied perspectives, more detailed description of the subject can be found in the books [1][2][3][4]. We note that most of the current results on the existence of fractional differential equations are focused on the finite interval, see [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. On the other hand, some authors have also focused on the solvability of fractional differential equations on the infinite intervals, some excellent results were obtained, see [24][25][26][27][28][29][30][31][32][33][34][35][36].…”