"A study of existence and multiplicity of positive solutions for nonlinear fractional differential equations with nonlocal boundary conditions"

Abstract

"This paper deals with the existence, uniqueness and the multiplicity of solutions for a class of fractional di erential equations boundary value prob- lems involving three-point nonlocal Riemann-Liouville fractional derivative and integral boundary conditions. Our results are based on some well-known tools of xed point theory such as Banach contraction principle, xed point index theory and the Leggett-Williams xed point theorem. As applications, some examples are presented at the end to illustrate the main results."

Existence of Solutions for Two-Point Integral Boundary Value Problems with Impulses

“…They include two, three, multi-point, and nonlocal boundary conditions as special cases. Various differential equations with several types of nonlocal conditions have been studied extensively and a large number of papers are devoted on this study, see [5,6,10,11,12,18,19,20,24] to mention a few.…”

Existence and Uniqueness for Fractional Differential Equations With Multipoint and Multi-Term Integral Boundary Conditions

“…Many scholars have studied the existence for nonlinear fractional differential equations with a variety boundary conditions by different approaches can easily be found in the literature on the topic. For some recent results, we can refer to [8][9][10][11][12][13][14] and references cited therein. However, most researchers tend to investigate either integral conditions or multi-point conditions, for example, in [15], the authors studied the existence of at least one, two or three positive solutions for the boundary value problem with three-point multi-term fractional integral boundary conditions (1.1) where is the standard Riemann-Liouville fractional derivative of order , is the Riemann-Liouville fractional integral of order , and , are real constants such that .…”