GENERALIZED FRACTIONAL HEAT EQUATION IN EXTENDED COLOMBEAU ALGEBRAS

Year 2026, Volume: 16 Issue: 1, 16 - 31, 08.01.2026

Abdelmjid Benmerrous Lalla Saadia Chadli M'hamed Elomari

Abstract

In this paper, we use the Colombeau generalized algebra to prove the existence and uniqueness of the solution of fractional heat equation with singular potentials (i.e., singular distributions). The concept of a generalized fractional semigroup was used to prove the result.

Keywords

Heat equation , Caputo derivative , Generalised solution , Semigroup , Singular potential

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