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

Volume 14, Issue 3, pp 124--138 http://dx.doi.org/10.22436/jnsa.014.03.02

Publication Date: September 16, 2020 Submission Date: June 24, 2020 Revision Date: August 07, 2020 Accteptance Date: August 17, 2020

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Authors

Ahmad Y. A. Salamooni - School of Mathematical Sciences, Swami Ramanand Teerth Marathwada University, Nanded-431606, India. D. D. Pawar - School of Mathematical Sciences, Swami Ramanand Teerth Marathwada University, Nanded-431606, India.

Abstract

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.

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Keywords

• Hilfer-Katugampola-type fractional derivative
• implicit differential equation
• Schaefer's fixed point theorem
• existence
• uniqueness
• Ulam stability

MSC

•  34A08
•  26A33
•  34B10
•  34A12

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