Existence and stability of Langevin equations with two Hilfer-Katugampola fractional derivatives

Authors

  • Rabha W. IBRAHIM Faculty of Computer Science and Information Technology University of Malaya, Kuala Lumpur 50603, Malaysia, e-mail: rabhaibrahim@yahoo.com https://orcid.org/0000-0001-9341-025X
  • Sugumaran HARIKRISHNAN Department of Mathematics Sri Ramakrishna Mission Vidyalaya College of Arts and Science Coimbatore-641020, India
  • Kuppusamy KANAGARAJAN Department of Mathematics Sri Ramakrishna Mission Vidyalaya College of Arts and Science Coimbatore-641020, India

DOI:

https://doi.org/10.24193/subbmath.2018.3.01

Keywords:

Fractional calculus, fractional differential operator, fractional differential equation, Ulam stability.

Abstract

In this note, we debate the existence, uniqueness and stability results for a general class of Langevin equations. We suggest the generalization via the Hilfer-Katugampola fractional derivative. We introduce some conditions for existence and uniqueness of solutions. We utilize the concept of fixed point theorems (Krasnoselskii fixed point theorem (KFPT), Banach contraction principle (BCP)). Moreover, we illustrate definitions of the Ulam type stability. These definitions generalize the fractional Ulam stability.

Mathematics Subject Classification (2010): 26A33, 49K40.

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Published

2018-09-20

How to Cite

IBRAHIM , R. W., HARIKRISHNAN, S., & KANAGARAJAN, K. (2018). Existence and stability of Langevin equations with two Hilfer-Katugampola fractional derivatives. Studia Universitatis Babeș-Bolyai Mathematica, 63(3), 291–302. https://doi.org/10.24193/subbmath.2018.3.01

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