# American Institute of Mathematical Sciences

October  2021, 14(10): 3337-3349. doi: 10.3934/dcdss.2020443

## Oscillation criteria for kernel function dependent fractional dynamic equations

 1 Department of Mathematics and General Sciences, Prince Sultan University, P. O. Box 66833, Riyadh 11586, Saudi Arabia 2 Department of Medical Research, China Medical University, Taichung 40402, Taiwan 3 Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan

Received  November 2019 Revised  March 2020 Published  October 2021 Early access  November 2020

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.

Citation: Bahaaeldin Abdalla, Thabet Abdeljawad. Oscillation criteria for kernel function dependent fractional dynamic equations. Discrete and Continuous Dynamical Systems - S, 2021, 14 (10) : 3337-3349. doi: 10.3934/dcdss.2020443
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