A survey on Hadamard and Hilfer fractional differential equations: Analysis and stability. (September 2017)

• Record Type: Journal Article
• Authors: Abbas, Saïd; Benchohra, Mouffak; Lazreg, Jamal-Eddine; Zhou, Yong
• Is Part Of: Chaos, solitons and fractals. Volume 102(2017)
• Page Start: 47
• Page End: 71
• Publication Date: 2017-09
• Subjects: Functional differential equation -- Pettis Riemann–Liouville integral of fractional order -- Hadamard fractional derivative -- Hilfer fractional derivative -- Solution -- Fixed point -- Weak solution -- Attractivity -- Ulam stability -- Measure of weak noncompactness; 26A33; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2017.03.010
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: In the present survey paper, we prove some results concerning the existence of solutions and weak solutions for some classes of Hadamard and Hilfer fractional differential equations. Some attractivity and Ulam stability results are presented. Our results are provided by applying the fixed point theory, and the technique of strong and weak measures of noncompactness.