Hyers – Ulam Stability Results for Discrete Antiperiodic Boundary Value Problem with Fractional Order 2 < 3
A. George Maria Selvam1, R. Dhineshbabu2
1A. George Maria Selvam*, Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur, Vellore – 632601, Tamil Nadu, India.
2R. Dhineshbabu, Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur, Vellore – 632601, Tamil Nadu, India.
Manuscript received on September 23, 2019. | Revised Manuscript received on October 15, 2019. | Manuscript published on October 30, 2019. | PP: 4997-5003 | Volume-9 Issue-1, October 2019 | Retrieval Number: A2123109119/2019©BEIESP| DOI: 10.35940/ijeat.A2123.109119
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: In this present work, we investigate Ulam stability for the following nonlinear discrete antiperiodic boundary value problem with fractional order of the form 0 ( ) = 1, ( 1) , C k v k k v k for 0 k L L [0, 2] = 0,1,…, 2 , with boundary conditions v v L ( 3) = ( ) , v v L ( 3) = ( ) , 2 2 v v L ( 3) = ( ) , where 2 :[ 2, ] L is a continuous and 0 C k is the Caputo fractional difference operator with order 2 < 3 . Finally, the main results are illustrated by some examples.
Keywords: Boundary Value Problem, Hyers – Ulam Stability, Caputo Fractional Derivative, Discrete Fractional Calculus.