Mohand transforms and its application to stability of differential equation
Authors
S. Baskaran
- Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur-635601, Tamil Nadu, India.
R. Murali
- Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur-635601, Tamil Nadu, India.
A. P. Selvan
- Department of Mathematics, Rajalakshmi Engineering College (Autonomous), Thandalam, Chennai - 602 105, Tamil Nadu, India.
Abstract
In this paper, we establish the Hyers-Ulam stability of a differential equation of higher order using a new transform technique called Mohand transforms.
Share and Cite
ISRP Style
S. Baskaran, R. Murali, A. P. Selvan, Mohand transforms and its application to stability of differential equation, Journal of Mathematics and Computer Science, 35 (2024), no. 1, 25--34
AMA Style
Baskaran S., Murali R., Selvan A. P., Mohand transforms and its application to stability of differential equation. J Math Comput SCI-JM. (2024); 35(1):25--34
Chicago/Turabian Style
Baskaran, S., Murali, R., Selvan, A. P.. "Mohand transforms and its application to stability of differential equation." Journal of Mathematics and Computer Science, 35, no. 1 (2024): 25--34
Keywords
- Hyers-Ulam stability
- differential equation
- Mohand transform
MSC
- 26D10
- 34A08
- 65Q30
- 42A38
- 39B82
- 34A40
References
-
[1]
M. R. Abdollahpour, R. Aghayari, M. Th. Rassias, Hyers-Ulam stability of associated Laguerre differential equations in a subclass of analytic functions, J. Math. Anal. Appl., 437 (2016), 605–612
-
[2]
M. R. Abdollahpour, M. Th. Rassias, Hyers-Ulam stability of hypergeometric differential equations, Aequationes Math., 93 (2019), 691–698
-
[3]
J. Acz´el, J. Dhombres, Functional equations in several variables, Cambridge University Press, Cambridge (1989)
-
[4]
Q. H. Alqifiary, S.-M. Jung, Laplace transform and generalized Hyers-Ulam stability of linear differential equations, Electron. J. Differential Equations, 2014 (2014), 11 pages
-
[5]
C. Alsina, R. Ger, On Some inequalities and stability results related to the exponential function, J. Inequal. Appl., 2 (1998), 373–380
-
[6]
T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan, 2 (1950), 64–66
-
[7]
P. S. Arumugam, G. Gandhi, S. Murugesan, V. Ramachandran, Laplace transform and Hyers-Ulam Stability of Differential Equation for Logistic growth in a population Model, Commun. Korean Math. Soc., 38 (2023), 1163–1173
-
[8]
D. G. Bourgin, Classes of transformations and bordering transformations, Bull. Amer. Math. Soc., 57 (1951), 223–237
-
[9]
N. Brillou¨et-Belluot, J. Brzde¸k, K. Ciepli ´ nski, On some recent developments in Ulam’s type stability, Abstr. Appl. Anal., 2012 (2012), 41 pages
-
[10]
A. Buakird, S. Saejung, Ulam stability with respect to a directed graph for some fixed point equations, Carpathian J. Math., 35 (2019), 23–30
-
[11]
S.-C. Chung, W.-G. Park, Hyers-Ulam stability of functional equations in 2-Banach spaces, Int. J. Math. Anal. (Ruse), 6 (2012), 951–961
-
[12]
S. Czerwik, Functional equations and inequalities in several variables, World Scientific Publishing Co., River Edge, NJ (2002)
-
[13]
R. Fukutaka, M. Onitsuka, Best constant in Hyers-Ulam stability of first-order homogeneous linear differential equations with a periodic coefficient, J. Math. Anal. Appl., 473 (2019), 1432–1446
-
[14]
Z. Gajda, On stability of additive mappings, Internat. J. Math. Math. Sci., 14 (1991), 431–434
-
[15]
P. G˘avrut¸a, On a problem of G. Isac and Th. M. Rassias concerning the stability of mappings, J. Math. Anal. Appl., 261 (2001), 543–553
-
[16]
D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A., 27 (1941), 222–224
-
[17]
D. H. Hyers, G. Isac, Th. M. Rassias, Stability of functional equations in several variables, Birkh¨auser Boston, Boston, MA (1998)
-
[18]
D. H. Hyers, Th. M. Rassias, Approximate homomorphisms, Aequationes Math., 44 (1992), 125–153
-
[19]
S.-M. Jung, Hyers-Ulam stability of linear differential equations of first order, Appl. Math. Lett., 17 (2004), 1135–1140
-
[20]
S.-M. Jung, Hyers-Ulam stability of linear differential equations of first order. III, J. Math. Anal. Appl., 311 (2005), 139–146
-
[21]
S.-M. Jung, Hyers-Ulam stability of linear differential equations of first order. II, Appl. Math. Lett., 19 (2006), 854–858
-
[22]
S.-M. Jung, Hyers-Ulam stability of a system of first order linear differential equations with constant coefficients, J. Math. Anal. Appl., 320 (2006), 549–561
-
[23]
S. M. Jung, Hyers-Ulam-Rassias stability of functional equations in nonlinear analysis, Springer, New York (2011)
-
[24]
S.-M. Jung, Approximate solutions of a linear differential equation of third order, Bull. Malays. Math. Sci. Soc. (2), 35 (2012), 1063–1073
-
[25]
S. M. Jung, M. Th. Rassias, A linear functional equation of third order associated to the Fibonacci numbers, Abstr. Appl. Anal., 2014 (2014), 7 pages
-
[26]
S.-M. Jung, D. Popa, M. Th. Rassias, On the stability of the linear functional equation in a single variable on complete metric groups, J. Global Optim., 59 (2014), 165–171
-
[27]
S.-M. Jung, M. Th. Rassias, C. Mortici, On a functional equation of trigonometric type, Appl. Math. Comput., 252 (2015), 294–303
-
[28]
S.-M. Jung, A. P. Selvan, M. Ramdoss, Mahgoub transform and Hyers-Ulam stability of first-order linear differential equations, J. Math. Inequal., 15 (2021), 1201–1218
-
[29]
S.-M. Jung, A. M. Sim˜ oes, A. P. Selvan, J. Roh, On the stability of Bessel differential equation, J. Appl. Anal. Comput., 12 (2022), 2014–2023
-
[30]
Pl. Kannappan, Functional equations and inequalities with applications, Springer, New York (2009)
-
[31]
Y.-H. Lee, S.-M. Jung, M. Th. Rassias, On an n-dimensional mixed type additive and quadratic functional equation, Appl. Math. Comput., 228 (2014), 13–16
-
[32]
Y.-H. Lee, S.-M. Jung, M. Th. Rassias, Uniqueness theorems on functional inequalities concerning cubic-quadratic-additive equation, J. Math. Inequal., 12 (2018), 43–61
-
[33]
T. Miura, On the Hyers-Ulam stability of a differentiable map, Sci. Math. Jpn., 55 (2002), 17–24
-
[34]
C. Mortici, M. Th. Rassias, S.-M. Jung, On the stability of a functional equation associated with the Fibonacci numbers, Abstr. Appl. Anal., 2014 (2014), 6 pages
-
[35]
R. Murali, A. P. Selvan, Mittag-Leffler-Hyers-Ulam Stability of a linear differential equations of first order using Laplace Transforms, Canad. J. Appl. Math., 2 (2020), 47–59
-
[36]
R. Murali, A. P. Selvan, Hyers-Ulam stability of a free and forced vibrations, Kragujevac J. Math., 44 (2020), 299–312
-
[37]
R. Murali, A. P. Selvan, S. Baskaran, C. Park, J. R. Lee, Hyers-Ulam stability of first-order linear differential equations using Aboodh transform, J. Inequal. Appl., 2021 (2021), 18 pages
-
[38]
R. Murali, A. P. Selvan, S. Baskaran, Stability of linear differential equation higher order using Mahgoub transforms, J. Math. Comput. Sci., 30 (2023), 1–9
-
[39]
R. Murali, A. P. Selvan, C. Park, J. R. Lee, Aboodh transform and the stability of second order linear differential equations, Adv. Difference Equ., 2021 (2021), 18 pages
-
[40]
M. Obłoza, Hyers stability of the linear differential equation, Rocznik Nauk.-Dydakt. Prace Mat., (1993), 259–270
-
[41]
M. Obłoza, Connections between Hyers and Lyapunov stability of the ordinary differential equations, Rocznik Nauk.- Dydakt. Prace Mat., 14 (1997), 141–146
-
[42]
C. Park, M. Th. Rassias, Additive functional equations and partial multipliers in C-algebras, Rev. R. Acad. Cienc. Exactas F´ıs. Nat. Ser. A Mat. RACSAM, 113 (2019), 2261–2275
-
[43]
M. Ramdoss, P. S. Arumugam, Fourier transforms and Ulam stabilities of linear differential equations, In: Frontiers in functional equations and analytic inequalities, Springer, Cham, (2019), 195–217
-
[44]
M. Ramdoss, P. Selvan-Arumugam, C. Park, Ulam stability of linear differential equations using Fourier transform, AIMS Math., 5 (2020), 766–780
-
[45]
Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297–300
-
[46]
Th. M. Rassias, On the stability of functional equations and a problem of Ulam, Acta. Appl. Math., 62 (2000), 23–130
-
[47]
A. P. Selvan, A. Najati, Hyers-Ulam stability and hyperstability of a Jensen-type functional equation on 2-Banach spaces, J. Inequal. Appl., 2022 (2022), 11 pages
-
[48]
A. P. Selvan, M. Onitsuka, Ulam type stabilities of n-th order linear differential equations using Gronwall’s inequality, Results Math., 78 (2023), 19 pages
-
[49]
A. SiBaha, B. Bouikhalene, E. Elquorachi, Ulam-Gˇavrutˇa-Rassias stability of a linear functional equation, Int. J. Appl. Math. Stat., 7 (2007), 157–166
-
[50]
A. Sim˜ oes, P. Selvan, Hyers-Ulam stability of a certain Fredholm integral equation, Turkish J. Math., 46 (2022), 87–98
-
[51]
S.-E. Takahasi, T. Miura, S. Miyajima, On the Hyers-Ulam stability of the Banach space-valued differential equation y0 = y, Bull. Korean Math. Soc., 39 (2002), 309–315
-
[52]
S. M. Ulam, Problems in modern mathematics, Science Editions John Wiley & Sons, New York (1964)
-
[53]
G. Wang, M. Zhou, L. Sun, Hyers-Ulam stability of linear differential equations of first order, Appl. Math. Lett., 21 (2008), 1024–1028
