Fractional integrals, derivatives and integral equations with weighted Takagi-Landsberg functions

03/30/2020
by   Vitalii Makogin, et al.
0

In this paper we find fractional Riemann-Liouville derivatives for the Takagi-Landsberg functions. Moreover, we introduce their generalizations called weighted Takagi-Landsberg functions which have arbitrary bounded coefficients in the expansion under Schauder basis. The class of the weighted Takagi- Landsberg functions of order H>0 on [0,1] coincides with the H-Hölder continuous functions on [0,1]. Based on computed fractional integrals and derivatives of the Haar and Schauder functions, we get a new series representation of the fractional derivatives of a Hölder continuous function. This result allows to get the new formula of a Riemann-Stieltjes integral. The application of such series representation is the new method of numerical solution of the Volterra and linear integral equations driven by a Hölder continuous function.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

03/18/2021

Shifted Monic Ultraspherical Approximation for solving some of Fractional Orders Differential Equations

The purpose of this paper is to show and explain a new formula that indi...
03/04/2017

Convex Geometry of the Generalized Matrix-Fractional Function

Generalized matrix-fractional (GMF) functions are a class of matrix supp...
06/21/2021

Python computations of general Heun functions from their integral series representations

We present a numerical implementation in Python of the recently develope...
02/02/2020

The Discrete Adjoint Method: Efficient Derivatives for Functions of Discrete Sequences

Gradient-based techniques are becoming increasingly critical in quantita...
11/26/2019

Recursive multivariate derivatives of e^f(x_1,..., x_n) of arbitrary order

High-order derivatives of nested functions of a single variable can be c...
12/16/2021

Dual Approach as Empirical Reliability for Fractional Differential Equations

Computational methods for fractional differential equations exhibit esse...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.