Existence and stability results of pantograph equation with three sequential fractional derivatives

[摘要] The subject of this work is the existence and Mittag-Leffler-Ulam (MLU) stability of solutions for fractional pantograph equations with three sequential fractional derivatives. Sufficient conditions for the existence and uniqueness of solutions are constructed by utilizing well-known classical fixed point theorems such as the Banach contraction principle, and Leray-Schauder nonlinear alternative. The generalized singular Gronwall's inequality is used to show the MLU stability results. An illustrated example is provided to support the main findings.

[学科分类] 地球科学(综合)

[关键词] fractional derivative;fixed point;existence;fractional pantograph equation;Mittag-Leffler-Ulam stability