Open AccessOn a nonlocal problem for a fourth-order mixed-type equation with the Hilfer operator
Author(s) -
B. J. Kadirkulov,
AUTHOR_ID,
Muhammadali Jalilov,
AUTHOR_ID
Publication year - 2021
Publication title -
ķaraġandy universitetìnìn̦ habaršysy. matematika seriâsy
Language(s) - English
Resource type - Journals
eISSN - 2663-5011
pISSN - 2518-7929
DOI - 10.31489/2021m4/89-102
Subject(s) - mathematics , uniqueness , operator (biology) , eigenfunction , type (biology) , mathematical analysis , initial value problem , stability (learning theory) , order (exchange) , cauchy problem , simple (philosophy) , eigenvalues and eigenvectors , philosophy , repressor , ecology , chemistry , computer science , biology , biochemistry , epistemology , quantum mechanics , machine learning , transcription factor , physics , finance , economics , gene
The present work is devoted to the study of the solvability questions for a nonlocal problem with an integrodifferential conjugation condition for a fourth-order mixed-type equation with a generalized RiemannLiouville operator. Under certain conditions on the given parameters and functions, we prove the theorems of uniqueness and existence of the solution to the problem. In the paper, given example indicates that if these conditions are violated, the formulated problem will have a nontrivial solution. To prove uniqueness and existence theorems of a solution to the problem, the method of separation of variables is used. The solution to the problem is constructed as a sum of an absolutely and uniformly converging series in eigenfunctions of the corresponding one-dimensional spectral problem. The Cauchy problem for a fractional equation with a generalized integro-differentiation operator is studied. A simple method is illustrated for finding a solution to this problem by reducing it to an integral equation equivalent in the sense of solvability. The authors of the article also establish the stability of the solution to the considered problem with respect to the nonlocal condition.