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Discontinuity, Nonlinearity, and Complexity 8(1) (2019) 37--48 | DOI:10.5890/DNC.2019.03.004

D. Vivek, K. Kanagarajan, S. Harikrishnan

Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore - 641020, Tamilnadu, India

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Abstract

A study on the existence and uniqueness of a solution for nonlinear neutral pantograph equations with Hilfer-Hadamard fractional derivative is the main aim of this paper. The existence result is obtained by using Schauder fixed point theorem. Also, we discuss Ulam stability for these equations based on Banach contraction principle.

Acknowledgments

This work was financially supported by the Tamilnadu State Council for Science and Technology, Dept. of Higher Education, Government of Tamilnadu. The authors are grateful to the referees for their careful reading of the manuscript and valuable comments. The authors thank the help from editor too.

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