On a Hilfer Type Fractional Differential Equation with Nonlinear Right-Hand Side

Authors

  • T. K. Yuldashev
  • B. J. Kadirkulov
  • A. R. Marakhimov

DOI:

https://doi.org/10.31489/2021m3/140-155

Keywords:

: Ordinary differential equation, equation with maxima, Hilfer operator, one-valued solvability, generalized Jacobi–Galerkin method

Abstract

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.

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Published

2021-09-30

Issue

Section

MATHEMATICS