Analytic Study on Nonlocal Initial Value Problems for Pantograph Equations with Hilfer-Hadamard Fractional Derivative


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Authors

  • D. Vivek Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore, Tamilnadu, India
  • K. Kanagarajan Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore, Tamilnadu, India
  • S. Harikrishnan Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore, Tamilnadu, India

Keywords:

Fractional pantograph equations, Hilfer fractional derivative, Existence, Fixed point, Ulam stability

Abstract

This paper is concerned with the existence and stability of solutions for a new class of nonlocal initial value problems involving Hilfer-Hadamrad type fractional pantograph equations. The existence results are obtained with the aid of some classical fixed point theorems, while the uniqueness of solutions is established by means of classical contraction mapping principle. We also discuss Ulam-Hyers stability for proposed problem.

 

Author Biographies

D. Vivek, Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore, Tamilnadu, India

 

 

K. Kanagarajan, Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore, Tamilnadu, India

 

 

S. Harikrishnan, Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore, Tamilnadu, India

 

 

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Published

15-05-2018

How to Cite

D. Vivek, K. Kanagarajan, & S. Harikrishnan. (2018). Analytic Study on Nonlocal Initial Value Problems for Pantograph Equations with Hilfer-Hadamard Fractional Derivative. International Journal of Mathematics And Its Applications, 6(2 - A), 21–32. Retrieved from http://ijmaa.in/index.php/ijmaa/article/view/636

Issue

Vol. 6 No. 2 - A (2018)

Section

Research Article

License

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