Boundary value problem for the heat equation with a load as the Riemann-Liouville fractional derivative

Арсен Владимирович Псху, M.T. Kosmakova, Dana M. Akhmanova, L.Zh. Kassymova, A.A. Assetov

BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, 2022

Full text Open access: Gold Metadata (CSL-JSON)

DOI 10.31489/2022m1/74-82

Data confidence 70 medium

How this score is calculated

It is built from checkable properties of the record itself: whether the article has a DOI, how many independent sources confirmed its data, whether the required fields are filled in, and how recent the latest confirmation is. Disagreement between sources and a missing identifier lower it. A value of 80 or above means the record was published without further checking; 60 to 79 means it is published at reduced confidence, with a manual check advisable. A record verified by an editor by hand is never pushed below 90 by a recalculation. This scores our data about the article, not the article itself.

Abstract

A boundary value problem for a fractionally loaded heat equation is considered in the first quadrant. The loaded term has the form of the Riemann-Liouville’s fractional derivative with respect to the time variable, and the order of the derivative in the loaded term is less than the order of the differential part. The study is based on reducing the boundary value problem to a Volterra integral equation. The kernel of the obtained integral equation contains a special function, namely, the Wright function. The kernel is estimated, and the conditions for the unique solvability of the integral equation are obtained.