Impulsive Hilfer fractional differential equations

Advances in Difference Equations

Hassan M. El-Owaidy¹  Mahmoud M. El-Borai²  Hamdy M. Ahmed³  Ahmed S. Ghanem³ 

[1] Department of Mathematics, Faculty of Science, Al-Azhar University;Department of Mathematics, Faculty of Science, Alexandria University;Higher Institute of Engineering, El-Shorouk Academy;

关键词: Impulsive condition;    Sobolev-type Hilfer fractional differential equation;    Controllability;    Approximate controllability;    Contraction mapping principle;   

DOI  :  10.1186/s13662-018-1679-7

来源: DOAJ

【 摘 要 】

Abstract Existence and controllability results for nonlinear Hilfer fractional differential equations are studied. Sufficient conditions for existence and approximate controllability for Sobolev-type impulsive fractional differential equations are established, where the time fractional derivative is the Hilfer derivative. An example for Sobolev-type Hilfer fractional delay partial differential equation with impulsive condition is considered.

【 授权许可】

Unknown