TY - JOUR
T1 - Vallée-Poussin theorem for fractional functional differential equations with integral boundary condition
AU - Domoshnitsky, Alexander
AU - Padhi, Seshadev
AU - Srivastava, Satyam Narayan
N1 - Publisher Copyright: © The Indian National Science Academy 2024.
PY - 2024
Y1 - 2024
N2 - This research paper focuses on the study of a Riemann-Liouville fractional functional differential equation and a linear continuous operator acting from the space of continuous functions to the space of essentially bounded functions with a boundary condition involving integral terms. We investigates the solvability and uniqueness of the equation under certain conditions on the coefficients. The paper utilizes techniques of Vallée-Poussin theorem, and Green’s function sign constancy to establish the main results. Choosing a corresponding function within the context of the Vallée-Poussin theorem results in explicit criteria presented as algebraic inequalities. These inequalities, as we illustrate through examples, cannot be further improved.
AB - This research paper focuses on the study of a Riemann-Liouville fractional functional differential equation and a linear continuous operator acting from the space of continuous functions to the space of essentially bounded functions with a boundary condition involving integral terms. We investigates the solvability and uniqueness of the equation under certain conditions on the coefficients. The paper utilizes techniques of Vallée-Poussin theorem, and Green’s function sign constancy to establish the main results. Choosing a corresponding function within the context of the Vallée-Poussin theorem results in explicit criteria presented as algebraic inequalities. These inequalities, as we illustrate through examples, cannot be further improved.
KW - 34K10
KW - 34K37
KW - 34K38
KW - 34K40
KW - Boundary value problems
KW - Differential inequality
KW - Fractional differential equations
KW - Riemann-Liouville derivative
KW - Sign constancy of Green’s function
UR - http://www.scopus.com/inward/record.url?scp=85196780784&partnerID=8YFLogxK
U2 - https://doi.org/10.1007/s13226-024-00621-4
DO - https://doi.org/10.1007/s13226-024-00621-4
M3 - مقالة
SN - 0019-5588
JO - Indian Journal of Pure and Applied Mathematics
JF - Indian Journal of Pure and Applied Mathematics
ER -