Nonlocal initial value problems for implicit differential equations with Hilfer–Hadamard fractional derivative
Articles
Devaraj Vivek
Sri Ramakrishna Mission Vidyalaya College of Arts and Science, India
Kuppusamy Kanagarajan
Sri Ramakrishna Mission Vidyalaya College of Arts and Science, India
Elsayed M. Elsayed
King Abdulaziz University; Mansoura University
Published 2018-06-15
https://doi.org/10.15388/NA.2018.3.4
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Keywords

Hilfer–Hadamard fractional derivative
implicit differential equations
fixed point
generalized Ulam–Hyers stability

How to Cite

Vivek D., Kanagarajan K. and Elsayed E. M. (2018) “Nonlocal initial value problems for implicit differential equations with Hilfer–Hadamard fractional derivative”, Nonlinear Analysis: Modelling and Control, 23(3), pp. 341-360. doi: 10.15388/NA.2018.3.4.

Abstract

In this paper, the Schaefer's fixed-point theorem is used to investigate the existence of solutions to nonlocal initial value problems for implicit differential equations with Hilfer–Hadamard fractional derivative. Then the Ulam stability result is obtained by using Banach contraction principle. An example is given to illustrate the applications of the main result.

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