Existence and oscillation results for the Hybrid generalized pantograph Hilfer fractional difference equation

Volume 36, Issue 1, pp 70--83 https://dx.doi.org/10.22436/jmcs.036.01.05

Publication Date: June 20, 2024 Submission Date: March 21, 2024 Revision Date: April 23, 2024 Accteptance Date: May 19, 2024

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Authors

S. Arundhathi - Department of Mathematics‎, Periyar University, Salem‎, ‎636011, Tamilnadu, ‎India. Dumitru Baleanu - Department of Computer Science and Mathematics, ‎Lebanese‎ ‎American University, ‎Beirut-11022801, ‎Lebanon. V. Muthulakshmi - Department of Mathematics‎, Periyar University, ‎Salem‎, ‎636011, Tamilnadu, India. Sh. S. Santra - JIS College of Engineering, Kalyani, West Bengal 741235, India.

Abstract

The objective of this study is to analyze the hybrid generalized pantograph Hilfer fractional difference equation's existence‎, ‎uniqueness and oscillatory behaviour‎. ‎Our technique‎, ‎in contrast to previous approaches in the literature‎, ‎is based on certain newly defined features of discrete fractional calculus and a few mathematical inequalities‎. ‎The hybrid fixed point theorem has been used to investigate the existence of solutions‎, ‎and the Banach contraction theorem has been used to show that the solution is unique‎. ‎Furthermore‎, ‎a set of adequate requirements is deduced to guarantee oscillation in the solutions of the hybrid generalized pantograph Hilfer fractional difference equation‎. ‎We provide two numerical simulations at the end of the article to demonstrate the effects of the main results‎. ‎

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Keywords

• Oscillation‎
• ‎hybrid
• pantograph
• Hilfer fractional difference operator

MSC

•  26A33
•  39A12
•  39A21

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