ULAM STABILITY FOR HILFER TYPE FRACTIONAL DIFFERENTIAL INCLUSIONS VIA THE WEAKLY PICARD OPERATORS THEORY

作者：Abbas Said^*; Benchohra Mouffak; Petrusel Adrian

来源：Fractional Calculus and Applied Analysis, 2017, 20(2): 384-398.

DOI：10.1515/fca-2017-0020

• fractional differential inclusion
• left-sided Riemann-Liouville integral of fractional order
• Hilfer fractional derivative
• multivalued weakly Picard operator
• fixed point inclusion
• Ulam-Hyers-Rassias stability

Considerable attention has been recently given to the existence of solutions of initial or boundary value problems for fractional differential equations and inclusions with Hilfer fractional derivative. Motivated by these results, in this paper we will present existence, data dependence and Ulam stability results for some differential inclusions with Hilfer fractional derivative. The results follow as applications of the multi-valued weakly Picard operator theory. An example illustrates the main result of the paper.

• 出版日期2017-4