Ulam–Hyers–Rassias Mittag-Leffler stability of ϖ–fractional partial differential equations

Abstract

Abstract This paper offers a comprehensive analysis of solution representations for ϖ-fractional partial differential equations, specifically focusing on the linear case of the Darboux problem. We exhibit a representation of the solutions for the Darboux problem of ϖ-fractional partial differential equations in the linear case in the space of continuous functions. Through the application of the generalized Gronwall inequality, we establish the Ulam–Hyers–Rassias Mittag–Leffler stability in the space of continuous functions. Three numerical examples are presented to show the effectiveness and the applicability of our results.

Keywords

• ϖ-Fractional integral
• ϖ-Caputo fractional derivative
• Hyers–Ulam stability
• Partial differential equations