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Browsing by Author "Ganesh, Anumanthappa"

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    Hyers-ulam-mittag-leffler stability of fractional differential equations with two caputo derivative using fractional fourier transform
    (2022) Ganesh, Anumanthappa; 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.
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    Sawi transform and Hyers-Ulam stability of nth order linear differential equations
    (2023) Jayapriya, Manickam; 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.