Existence and uniqueness results for mixed derivative involving fractional operators

[摘要] In this article, we discuss the existence and uniqueness results for mix derivative involving fractional operators of order $ \beta\in (1, 2) $ and $ \gamma\in (0, 1) $. We prove some important results by using integro-differential equation of pantograph type. We establish the existence and uniqueness of the solutions using fixed point theorem. Furthermore, one application is likewise given to represent our fundamental results.

[学科分类] 地球科学(综合)

[关键词] fractional derivatives;existence conditions;integro-differential equations;pantograph equations