Existence and uniqueness of solution for a fractional thixotropic model

Abstract

In this work, we study the existence and uniqueness of solutions of the fractional thixotropic problem in one‐dimensional case. The problem of thixotropic was studied by many researchers. But our study is focussed on the fractional derivative , which is a new addition to the previous works of thixotropic problem. So, in this work, we based on two parts: The first is studding the existence and uniqueness of solutions of the modified fractional thixotropic model using regularization, some prior estimates, and Gronwall's lemma. The second is proving that the problem converges to the fractional thixotropic model by using fixed point theorem.