Positive Solutions for a Three-Point Boundary Value Problem of Fractional Q-Difference Equations

Abstract

In this work, a three-point boundary value problem of fractional q-difference equations is discussed. By using fixed point theorems on mixed monotone operators, some sufficient conditions that guarantee the existence and uniqueness of positive solutions are given. In addition, an iterative scheme can be made to approximate the unique solution. Finally, some interesting examples are provided to illustrate the main results.

Investigation of Ulam Stability Results of a Coupled System of Nonlinear Implicit Fractional Differential Equations

“…Since we supposed that u n → u, then v n → v as n → 8 for each t ∈ J , by the Lebesgue dominated convergence theorem, (10) implies that:…”

“…Several researchers have built up some attention-grabbing results of the existence of solutions to boundary value problems for FODE by using standard fixed point theorems. For a detailed study, see [8][9][10] and the references cited therein. However, the study of coupled systems of differential equations of different orders is also very significant because this kind of system appears in different problems of an applied nature; see [11][12][13][14][15][16][17][18][19] and the references cited therein.…”

Hilfer Fractional Quantum Derivative and Boundary Value Problems

“…Recent treatment on such material can be found in [7]. Research on the topic has yield variety of new results in recent years, as seen in [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] and references therein.…”

A New Approach of Morgan-Voyce Polynomial to Solve Three Point Boundary Value Problems

“…This local boundary value problem has a major role in physics, engineering and many phenomena in applied mathematical. An amount of research has been studying the three-point boundary value problem, for example, the positive solution [1], existence and stability [2], discrete first order [3], and variational principle [4].…”