On partial fractional Sturm–Liouville equation and inclusion

• Main Authors: Zohreh Zeinalabedini Charandabi, Hakimeh Mohammadi, Shahram Rezapour, Hashem Parvaneh Masiha
• Format: Article
• Language: English
• Published: SpringerOpen 2021-07-01
• Series: Advances in Difference Equations
• Subjects: α-ψ-contractive map; Inclusion problem; The Caputo derivative; The partial fractional Sturm–Liouville equation; Two variables partial differential equation
• Online Access: https://doi.org/10.1186/s13662-021-03478-7
• ISSN: 1687-1847

Abstract 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.