Open AccessOscillation criteria for kernel function dependent fractional dynamic equations
Author(s) -
Bahaaeldin Abdalla,
Thabet Abdeljawad
Publication year - 2021
Publication title -
discrete and continuous dynamical systems. series s
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 34
eISSN - 1937-1632
pISSN - 1937-1179
DOI - 10.3934/dcdss.2020443
Subject(s) - oscillation (cell signaling) , mathematics , kernel (algebra) , quadratic equation , function (biology) , fractional calculus , mathematical analysis , quadratic function , type (biology) , class (philosophy) , pure mathematics , computer science , ecology , genetics , geometry , evolutionary biology , artificial intelligence , biology
In this work, we examine the oscillation of a class fractional differential equations in the frame of generalized nonlocal fractional derivatives with function dependent kernel type. We present sufficient conditions to prove the oscillation criteria in both of the Riemann-Liouville (RL) and Caputo types. Taking particular cases of the nondecreasing function appearing in the kernel of the treated fractional derivative recovers the oscillation of several proven results investigated previously in literature. Two examples, where the kernel function is quadratic and cubic polynomial, have been given to support the validity of the proven results for the RL and Caputo cases, respectively.