Positive Solutions for a Higher-Order Semipositone Nonlocal Fractional Differential Equation with Singularities on Both Time and Space Variable

Positive Solutions for a Higher-Order Semipositone Nonlocal Fractional Differential Equation with Singularities on Both Time and Space Variable

In this paper, we consider the following higher-order semipositone nonlocal Riemann-Liouville fractional differential equation D0+αx(t)+f(t,x(t),D0+βx(t))+e(t)=0,  0<t<1,D0+βx(0)=D0+β+1x(0)=⋯=D0+n+β-2x(0)=0, and D0+βx(1)=∑i=1m-2ηiD0+βx(ξi), where D0+α and D0+β are the standard Riemann-Liouvill...

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Main Author: Kemei Zhang
Format: Article
Language:English
Published: Hindawi Limited 2019-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2019/7161894
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spelling doaj-b68a5191146447fbbe9501bfd24963192020-11-24T23:56:35ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882019-01-01201910.1155/2019/71618947161894Positive Solutions for a Higher-Order Semipositone Nonlocal Fractional Differential Equation with Singularities on Both Time and Space VariableKemei Zhang0School of Mathematics Sciences, Qufu Normal University, Qufu 273165, Shandong, ChinaIn this paper, we consider the following higher-order semipositone nonlocal Riemann-Liouville fractional differential equation D0+αx(t)+f(t,x(t),D0+βx(t))+e(t)=0,  0<t<1,D0+βx(0)=D0+β+1x(0)=⋯=D0+n+β-2x(0)=0, and D0+βx(1)=∑i=1m-2ηiD0+βx(ξi), where D0+α and D0+β are the standard Riemann-Liouville fractional derivatives. The existence results of positive solution are given by Guo-krasnosel’skii fixed point theorem and Schauder’s fixed point theorem.http://dx.doi.org/10.1155/2019/7161894
collection DOAJ
language English
format Article
sources DOAJ
author Kemei Zhang
spellingShingle Kemei Zhang
Positive Solutions for a Higher-Order Semipositone Nonlocal Fractional Differential Equation with Singularities on Both Time and Space Variable
Journal of Function Spaces
author_facet Kemei Zhang
author_sort Kemei Zhang
title Positive Solutions for a Higher-Order Semipositone Nonlocal Fractional Differential Equation with Singularities on Both Time and Space Variable
title_short Positive Solutions for a Higher-Order Semipositone Nonlocal Fractional Differential Equation with Singularities on Both Time and Space Variable
title_full Positive Solutions for a Higher-Order Semipositone Nonlocal Fractional Differential Equation with Singularities on Both Time and Space Variable
title_fullStr Positive Solutions for a Higher-Order Semipositone Nonlocal Fractional Differential Equation with Singularities on Both Time and Space Variable
title_full_unstemmed Positive Solutions for a Higher-Order Semipositone Nonlocal Fractional Differential Equation with Singularities on Both Time and Space Variable
title_sort positive solutions for a higher-order semipositone nonlocal fractional differential equation with singularities on both time and space variable
publisher Hindawi Limited
series Journal of Function Spaces
issn 2314-8896
2314-8888
publishDate 2019-01-01
description In this paper, we consider the following higher-order semipositone nonlocal Riemann-Liouville fractional differential equation D0+αx(t)+f(t,x(t),D0+βx(t))+e(t)=0,  0<t<1,D0+βx(0)=D0+β+1x(0)=⋯=D0+n+β-2x(0)=0, and D0+βx(1)=∑i=1m-2ηiD0+βx(ξi), where D0+α and D0+β are the standard Riemann-Liouville fractional derivatives. The existence results of positive solution are given by Guo-krasnosel’skii fixed point theorem and Schauder’s fixed point theorem.
url http://dx.doi.org/10.1155/2019/7161894
work_keys_str_mv AT kemeizhang positivesolutionsforahigherordersemipositonenonlocalfractionaldifferentialequationwithsingularitiesonbothtimeandspacevariable
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