TY - JOUR

T1 - Vallée-Poussin theorem for Hadamard fractional functional differential equations

AU - Bohner, Martin

AU - Domoshnitsky, Alexander

AU - Litsyn, Elena

AU - Padhi, Seshadev

AU - Narayan Srivastava, Satyam

N1 - Publisher Copyright:
© 2023 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.

PY - 2023

Y1 - 2023

N2 - We propose necessary and sufficient conditions for the negativity of the two-point boundary value problem in the form of the Vallée-Poussin theorem about differential inequalities for the Hadamard fractional functional differential problem (Formula presented.) Here, the operator (Formula presented.) can be an operator with deviation (of delayed or advanced type), an integral operator or various linear combinations and superpositions. For example, the operator can be of the forms (Formula presented.), (Formula presented.) or (Formula presented.). We obtain explicit tests of negativity of Green's function in the form of algebraic inequalities. Our paper is the first one where a general form of the operator is considered with Hadamard fractional derivatives.

AB - We propose necessary and sufficient conditions for the negativity of the two-point boundary value problem in the form of the Vallée-Poussin theorem about differential inequalities for the Hadamard fractional functional differential problem (Formula presented.) Here, the operator (Formula presented.) can be an operator with deviation (of delayed or advanced type), an integral operator or various linear combinations and superpositions. For example, the operator can be of the forms (Formula presented.), (Formula presented.) or (Formula presented.). We obtain explicit tests of negativity of Green's function in the form of algebraic inequalities. Our paper is the first one where a general form of the operator is considered with Hadamard fractional derivatives.

KW - Green's function

KW - Hadamard fractional derivative

KW - Vallée-Poussin theorem

KW - differential inequality

KW - existence and uniqueness

KW - two-point fractional boundary value problem

UR - http://www.scopus.com/inward/record.url?scp=85173603658&partnerID=8YFLogxK

U2 - 10.1080/27690911.2023.2259057

DO - 10.1080/27690911.2023.2259057

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AN - SCOPUS:85173603658

SN - 2769-0911

VL - 31

JO - Applied Mathematics in Science and Engineering

JF - Applied Mathematics in Science and Engineering

IS - 1

M1 - 2259057

ER -