Browsing by Author "Santra, Shyam Sundar"

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First-order impulsive differential systems: sufficient and necessary conditions for oscillatory or asymptotic behavior
(2021) Baleanu, Dumitru; Baleanu, Dumitru; Khedher, Khaled Mohamed; 56389
In this paper, we study the oscillatory and asymptotic behavior of a class of first-order neutral delay impulsive differential systems and establish some new sufficient conditions for oscillation and sufficient and necessary conditions for the asymptotic behavior of the same impulsive differential system. To prove the necessary part of the theorem for asymptotic behavior, we use the Banach fixed point theorem and the Knaster–Tarski fixed point theorem. In the conclusion section, we mention the future scope of this study. Finally, two examples are provided to show the defectiveness and feasibility of the main results. © 2021, The Author(s).
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.
Numerical analysis of fractional order discrete Bloch equations
(2024) Baleanu, Dumitru; Santra, Shyam Sundar; Jayanathan, Leo Amalraj; Baleanu, Dumitru; 56389
By defining a new kind of h-extorial function with constant coefficient, this research seeks to solve discrete fractional Bloch equations. By using an extorial function of the Mittag-Leffler type, we are able to discover the general solutions for the magnetization’s Bx, By, and Bz components. These findings demonstrate the innovative method of fractional order Bloch equations. In addition, we offer a graphical representation of our results.
Oscillation criteria for a class of half-linear neutral conformable differential equations
(2023) Baleanu, Dumitru; Kavitha, Jayapal; Sadhasivam, Vadivel; Baleanu, Dumitru; 56389
The main aim of this note is to obtain new oscillation criteria for a certain class of half-linear neutral conformable differential equations by the method of comparison and Riccati transformation technique. A suitable example is given to illustrate our new results.
Sawi transform and Hyers-Ulam stability of nth order linear differential equations
(2023) Baleanu, Dumitru; Ganesh, Anumanthappa; Santra, Shyam Sundar; Edwan, Reem; Baleanu, Dumitru; Khedher, Khaled Mohamed; 56389
The use of the Sawi transform has increased in the light of recent events in different approaches. The Sawi transform is also seen as the easiest and most effective way among the other transforms. In line with this, the research deals with the Hyers-Ulam stability of nth order differential equations using the Sawi transform. The study aims at deriving a generalised Hyers-Ulam stability result for linear homogeneous and non-homogeneous differential equations.
Solving fractional integro-differential equations by Aboodh transform
(2024) Baleanu, Dumitru; Gunasekar, Tharmalingam; Balasundaram, Hemalatha; Santra, Shyam Sundar; Majumder, Debasish; Baleanu, Dumitru; 56389
This study approaches some families of fractional integro-differential equations (FIDEs) using a simple fractional calculus method, which leads to several appealing consequences, including the classical Frobenius method, which is generalized. The method presented here is based mostly on certain general theorems on particular solutions of FIDEs using the Aboodh transform and binomial series extension coefficients. We additionally demonstrate techniques to solve FIDEs.