Open AccessOn a Hilfer Type Fractional Differential Equation with Nonlinear Right-Hand Side
Author(s) -
T. K. Yuldashev,
B. J. Kadirkulov,
A. R. Marakhimov
Publication year - 2021
Publication title -
ķaraġandy universitetìnìn̦ habaršysy. matematika seriâsy
Language(s) - English
Resource type - Journals
eISSN - 2663-5011
pISSN - 2518-7929
DOI - 10.31489/2021m3/140-155
Subject(s) - mathematics , uniqueness , nonlinear system , type (biology) , mathematical analysis , fractional calculus , realization (probability) , initial value problem , galerkin method , volterra integral equation , transformation (genetics) , differential equation , integral equation , ecology , biochemistry , statistics , physics , chemistry , quantum mechanics , gene , biology
In this article we consider the questions of one-valued solvability and numerical realization of initial value problem for a nonlinear Hilfer type fractional differential equation with maxima. By the aid of uncomplicated integral transformation based on Dirichlet formula, this initial value problem is reduced to the nonlinear Volterra type fractional integral equation. The theorem of existence and uniqueness of the solution of given initial value problem in the segment under consideration is proved. For numerical realization of solution the generalized Jacobi–Galerkin method is applied. Illustrative examples are provided.