Browsing by Author "Govindan, Vediyappan"

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General solution and generalized Hyers-Ulam stability for additive functional equations
(2023) Baleanu, Dumitru; Arulselvam, Manimaran; Baleanu, Dumitru; Govindan, Vediyappan; Khedher, Khaled Mohamed; 56389
In this paper, we introduce new types of additive functional equations and obtain the solutions to these additive functional equations. Furthermore, we investigate the Hyers-Ulam stability for the additive functional equations in fuzzy normed spaces and random normed spaces using the direct and fixed point approaches. Also, we will present some applications of functional equations in physics. Through these examples, we explain how the functional equations appear in the physical problem, how we use them to solve it, and we talk about solutions that are not used for solving the problem, but which can be of interest. We provide an example to show how functional equations may be used to solve geometry difficulties.
Hyers-ulam-mittag-leffler stability of fractional differential equations with two caputo derivative using fractional fourier transform
(2022) Baleanu, Dumitru; Deepa, Swaminathan; Baleanu, Dumitru; Santra, Shyam Sundar; Moaaz, Osama; Govindan, Vediyappan; Ali, Rifaqat; 56389
In this paper, we discuss standard approaches to the Hyers-Ulam Mittag Leffler problem of fractional derivatives and nonlinear fractional integrals (simply called nonlinear fractional differential equation), namely two Caputo fractional derivatives using a fractional Fourier transform. We prove the basic properties of derivatives including the rules for their properties and the conditions for the equivalence of various definitions. Further, we give a brief basic Hyers-Ulam Mittag Leffler problem method for the solving of linear fractional differential equations using fractional Fourier transform and mention the limits of their usability. In particular, we formulate the theorem describing the structure of the Hyers-Ulam Mittag Leffler problem for linear two-term equations. In particular, we derive the two Caputo fractional derivative step response functions of those generalized systems. Finally, we consider some physical examples, in the particular fractional differential equation and the fractional Fourier transform. © 2022 the Author(s), licensee AIMS Press.
Oscillation result for half-linear delay di erence equations of second-order
(2022) Baleanu, Dumitru; Santra, Shyam Sunda; Baleanu, Dumitru; Edwan, Reem; Govindan, Vediyappan; Murugesan, Arumugam; Altanji, Mohamed; 56389
In this paper, we obtain the new single-condition criteria for the oscillation of secondorder half-linear delay difference equation. Even in the linear case, the sharp result is new and, to our knowledge, improves all previous results. Furthermore, our method has the advantage of being simple to prove, as it relies just on sequentially improved monotonicities of a positive solution. Examples are provided to illustrate our results.