Mathematics and Computational Sciences

Existence, regularity, and asymptotic analysis for conformable parabolic equations with history-dependent diffusion

Articles in Press

Document Type : Original Article

Authors

Lan Nhu Nguyen
Luc Hoang Nguyen
Hai Minh Nguyen
Vinh Quang Mai

Department of Economic Mathematics, Faculty of Data Science in Business, Ho Chi Minh University of Banking, Ho Chi Minh City, Vietnam

10.30511/mcs.2026.2069393.1449
Abstract
This paper investigates a diffusion equation incorporating memory effects and a conformable fractional derivative. We begin by deriving an explicit representation of the mild solution and analyzing its regularity properties. Next, we explore the continuous dependence of the solution on key parameters, highlighting its sensitivity to changes. As the order of the conformable derivative approaches one, we demonstrate that the mild solution converges to that of the classical diffusion equation. Furthermore, we establish a finite-time blow-up criterion under specific nonlinear conditions. Employing fixed-point theorems, we prove the existence and uniqueness of mild solutions and identify the conditions necessary to ensure these results. Our findings offer new insights into how conformable fractional derivatives and memory terms influence solution behavior and stability.

Keywords

Conformable derivative
Memory terms
Mild solution
Regularity
Blow-up criterion
Subjects
Mathematics and Computational Sciences

Articles in Press, Accepted Manuscript
Available Online from 23 May 2026

  • Receive Date 20 August 2025
  • Revise Date 18 May 2026
  • Accept Date 23 May 2026

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