Functions of finite fractional variation and their applications to fractional impulsive equations

Czechoslovak Mathematical Journal

Dariusz Idczak¹ 

关键词: finite fractional variation;    weak $\sigma$-additive fractional;    derivative;    fractional impulsive equation;    Dirac measure;    Cauchy formula;   

DOI  :  10.21136/CMJ.2017.0455-15

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

  We introduce a notion of a function of finite fractional variation and characterize such functions together with their weak $\sigma$-additive fractional derivatives. Next, we use these functions to study differential equations of fractional order, containing a $\sigma$-additive term - we prove existence and uniqueness of a solution as well as derive a Cauchy formula for the solution. We apply these results to impulsive equations, i.e.\^^Mequations containing the Dirac measures.

【 授权许可】

Unknown