Vallée-Poussin Theorem for Hadamard Fractional Functional Differential Equations
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.
M. Bohner et al., "Vallée-Poussin Theorem for Hadamard Fractional Functional Differential Equations," Applied Mathematics in Science and Engineering, vol. 31, no. 1, article no. 2259057, Taylor and Francis Group; Taylor and Francis, Jan 2023.
The definitive version is available at https://doi.org/10.1080/27690911.2023.2259057
Mathematics and Statistics
Keywords and Phrases
differential inequality; existence and uniqueness; Green's function; Hadamard fractional derivative; two-point fractional boundary value problem; Vallée-Poussin theorem
International Standard Serial Number (ISSN)
Article - Journal
© 2023 The Authors, All rights reserved.
01 Jan 2023