This paper is devoted to the study of existence and uniqueness of a mild solution for a parabolic equation with conformable derivative. The nonlocal problem for parabolic equations appears in many various applications, such as physics, biology. The first part of this paper is to consider the well-posedness and regularity of the mild solution. The second one is to investigate the existence by using Banach fixed point theory.

中文翻译：

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关于系数与时间有关的抛物方程的一个非局部问题

本文致力于研究具有相容导数的抛物方程的温和解的存在性和唯一性。抛物线方程的非局部问题出现在许多应用中，例如物理，生物学。本文的第一部分是考虑温和解的适定性和规则性。第二个是使用Banach不动点理论研究其存在性。