Limit properties of positive solutions of fractional boundary value problems

Staněk, Svatoslav

doi:10.1016/j.amc.2012.09.008

Cited by 3 publications

(3 citation statements)

References 25 publications

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“…We note that in [24], the relation between solutions of the sequence of regular fractional BVPs Our paper is organized as follows. Section 2 contains the results from the fractional calculus and the technical lemmas that are used in the next sections.…”

Section: S Staněkmentioning

confidence: 99%

Fractional BVPs with strong time singularities and the limit properties of their solutions

Staněk¹

2014

Open Mathematics

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Section: S Staněkmentioning

confidence: 99%

Fractional BVPs with strong time singularities and the limit properties of their solutions

Staněk¹

2014

Open Mathematics

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“…For some recent works on nonlocal fractional boundary value problems, we refer the reader to the papers [7][8][9][10][11], while the results based on monotone method for such problems can be found in [12,13]. In [14], the limit properties of positive solutions of fractional boundary value problems have been discussed.…”

Section: Introductionmentioning

confidence: 99%

New Existence Results for Fractional Integrodifferential Equations with Nonlocal Integral Boundary Conditions

Cao¹,

Alsaedi²,

Ntouyas³

et al. 2015

Abstract and Applied Analysis

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We consider a boundary value problem of fractional integrodifferential equations with new nonlocal integral boundary conditions of the form: (0) = ( ), ( ) = ∫ 1 ( ) , and 0 < < < < 1. According to these conditions, the value of the unknown function at the left end point = 0 is proportional to its value at a nonlocal point while the value at an arbitrary (local) point is proportional to the contribution due to a substrip of arbitrary length (1 − ). These conditions appear in the mathematical modelling of physical problems when different parts (nonlocal points and substrips of arbitrary length) of the domain are involved in the input data for the process under consideration. We discuss the existence of solutions for the given problem by means of the Sadovski fixed point theorem for condensing maps and a fixed point theorem due to O'Regan. Some illustrative examples are also presented.

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“…There has been a significant development in ordinary and partial fractional differential equations in recent years; see the monographs of Abbas et al [7,8], Baleanu et al [14], Kilbas et al [29], the papers of Abbas et al [1][2][3][4][5][6]9, 10], Ahmad and Nieto [11], Czlapinski [21,22], Kilbas and Marzan [28], Stanek [41], Vityuk and Golushkov [44], and the references therein.…”

Section: Introductionmentioning

confidence: 99%