On partial fractional Sturm–Liouville equation and inclusion

[摘要] The Sturm–Liouville differential equation is one of interesting problems which has been studied by researchers during recent decades. We study the existence of a solution for partial fractional Sturm–Liouville equation by using the α-ψ-contractive mappings. Also, we give an illustrative example. By using the α-ψ-multifunctions, we prove the existence of solutions for inclusion version of the partial fractional Sturm–Liouville problem. Finally by providing another example and some figures, we try to illustrate the related inclusion result.

[学科分类] 航空航天科学

[关键词] α;ψ -contractive map;Inclusion problem;The Caputo derivative;The partial fractional Sturm–Liouville equation;Two variables partial differential equation