Existence and stability results for Hilfer-Katugampola-type fractional implicit differential equations with nonlocal conditions

The Journal of Nonlinear Sciences and its Applications

article

Ahmad Y. A. Salamooni¹  D. D. Pawar¹ 

[1] School of Mathematical Sciences, Swami Ramanand Teerth Marathwada University

关键词: Hilfer-Katugampola-type fractional derivative;    implicit differential equation;    Schaefer's fixed point theorem;    existence;    uniqueness;    Ulam stability;   

DOI  :  10.22436/jnsa.014.03.02

学科分类：社会科学、人文和艺术（综合）

来源: Shomal University

【 摘 要 】

This article contains a new discussion for Hilfer-Katugampola-type fractional derivative. We establish an existence and uniqueness results of Hilfer-Katugampola-type fractional derivative for implicit differential equations with the help of Schaefer's fixed point theorem and Banach contraction principle. Also, we use the Gronwall's lemma for singular kernels to prove the Ulam-Hyers-Rassias stability results. Further, the examples are given to illustrate our main results.

【 授权许可】

Unknown