Existence, Uniqueness and Stability of Hilfer Type Neutral Pantograph Differential Equations with Nonlocal Conditions

D. Vivek; E. M. Elsayed; K. Kanagarajan

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International Journal of Scientific and Innovative Mathematical Research

Volume 6, Issue 8, 2018, Page No:42-53

Existence, Uniqueness and Stability of Hilfer Type Neutral Pantograph Differential Equations with Nonlocal Conditions

D. Vivek¹, E. M. Elsayed^2*, K. Kanagarajan³

1.Department of Mathematics CA, Sri Ramakrishna College of Arts and Science, Coimbatore-641006, India.
2.Department of Mathematics, Faculty of Science,King Abdulaziz University, Jeddah, Saudi Arabia. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt.
3.Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science,Coimbatore, India.

Citation : D. Vivek, E. M. Elsayed, K. Kanagarajan, Existence, Uniqueness and Stability of Hilfer Type Neutral Pantograph Differential Equations with Nonlocal Conditions International Journal of Scientific and Innovative Mathematical Research 2018 , 6(8) : 42-53.

Abstract

A study on dynamics and stability of nonlinear neutral pantograph equations with Hilfer fractional derivative is the main aim of this paper. The existence result is obtained by using Scheafer's fixed point theorem. In addition we discuss Ulam stability of the system by employing Banach contraction principle.

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