Existence and Uniqueness of Positive Solutions of Boundary-Value Problems for Fractional Differential Equations with p-Laplacian Operator and Identities on the Some Special Polynomials

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dc.authorid0000-0002-8848-0058
dc.authorid0000-0001-6603-2652
dc.authorid0000-0001-6603-2652
dc.authorid0000-0003-1091-9697
dc.authorid0000-0002-3950-6864
dc.authorid0000-0003-1091-9697
dc.authorscopusid55539330800
dc.authorscopusid26657919900
dc.authorscopusid35249182600
dc.authorscopusid35179145500
dc.authorscopusid6506228517
dc.authorwosidOruçoğlu, Kamil/ABH-4956-2020
dc.authorwosidŞen, Erdoğan/J-7484-2017
dc.authorwosidAÇIKGÖZ, MEHMET/F-7527-2019
dc.authorwosidSen, Erdogan/ABA-5139-2020
dc.authorwosidAraci, Serkan/P-4355-2015
dc.authorwosidAcikgoz, Mehmet/AAH-2493-2020
dc.contributor.authorŞen, Erdoğan
dc.contributor.authorAçıkgöz, Mehmet
dc.contributor.authorSeo, Jong Jin
dc.contributor.authorAracı, Serkan
dc.contributor.authorOruçoğlu, Kamil
dc.date.accessioned2022-05-11T14:31:12Z
dc.date.available2022-05-11T14:31:12Z
dc.date.issued2013
dc.departmentFakülteler, Fen Edebiyat Fakültesi, Matematik Bölümü
dc.description.abstractWe consider the following boundary- value problem of nonlinear fractional differential equation with p-Laplacian operator D-0+(beta)(phi(p)(D(0+)(alpha)u(t))) + a(t)f(u) = 0, 0 < t < 1, u(0) = gamma u(h) + lambda, u'(0) = mu, phi(p)(D(0+)(alpha)u(0)) = (phi(p)(D-0+(alpha) u(0)) = (phi(p)(D(0+)(alpha)u(1)))' = (phi(p)(D(0+)(alpha)u(0)))'' = (phi(p)(D(0+)(alpha)u(0)))''' = 0, where 1 < alpha <= 2, 3 < beta <= 4 are real numbers are real numbers, D-0+(alpha), D-0+(beta) are the standard Caputo fractional derivatives, phi(p)(s) = vertical bar s vertical bar(p-2)s. p > 1, phi(-1)(p) = phi(q), 1/p + 1/q = 1, 0 <= gamma < 1, 0 <= h <= 1, lambda, mu > 0 are parameters a : (0, 1) -> [0, +infinity), and f : [ 0, +infinity) -> [0, +infinity) are continuous. By the properties of Green function and Schauder fixed point theorem, several existence and nonexistence results for positive solutions, in terms of the parameters.. and.. are obtained. The uniqueness of positive solution on the parameters lambda and mu is also studied. In the final section of this paper, we derive not only new but also interesting identities related special polynomials by which Caputo fractional derivative.
dc.identifier.doi10.1155/2013/753171
dc.identifier.issn2090-8997
dc.identifier.issn0972-6802
dc.identifier.scopus2-s2.0-84890033873
dc.identifier.scopusqualityN/A
dc.identifier.urihttps://doi.org/10.1155/2013/753171
dc.identifier.urihttps://hdl.handle.net/20.500.11776/7361
dc.identifier.wosWOS:000327622600001
dc.identifier.wosqualityQ2
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.institutionauthorŞen, Erdoğan
dc.language.isoen
dc.publisherHindawi Ltd
dc.relation.ispartofJournal of Function Spaces and Applications
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccess
dc.subjectTheorem
dc.titleExistence and Uniqueness of Positive Solutions of Boundary-Value Problems for Fractional Differential Equations with p-Laplacian Operator and Identities on the Some Special Polynomials
dc.typeArticle

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