Application of the sumudu transform to some equations with fractional derivatives

Abstract

Keywords: Fractional Differential Equations; Sumudu Transform; Inverse Sumudu Transform

References

1. Acay B, Bas E, Abdeljawad T. Fractional economic models based on market equilibrium in the frame of different type kernels. Chaos, Solit Fractals 2020;130:109438. [CrossRef]
2. Ahmed SA. Applications of New Double Integral Transform (Laplace-Sumudu Transform) in Mathematical Physics. In Abstract and Applied Figure 14. Analysis for Atangana – Baleanu derivative. Analysis. 2021;2021. Hindawi. [CrossRef] Sigma J Eng Nat Sci, Vol. 41, No. 6, pp. 1132−1143, December, 2023 1143
3. Al-Humedi HO, Kadhim SAH. Solution of lin- [16] Belgacem FBM, Karaballi AA, et al. Analytical inves- ear fuzzy fractional differential equations using tigations of the Sumudu transform and applications fuzzy natural transform. Earthline J Math Sci to integral production equations. Math Problems 2022;8:41−65. [CrossRef] Eng 2003;2003:103−118. [CrossRef]
4. Aibinu MO, Moyo SC, Moyo S. Analyzing pop- [17] Bhargava A, Jain RK, et al. A Comparative Study ulation dynamics models via Sumudu trans- of Laplace Transform and Sumudu Transform form. arXiv [Epub ahead of print]. doi: 10.48550/ on-Function. In IOP Conference Series: Materials arXiv.2112.07126 Science and Engineering. 2021;1099(1):012024. IOP
5. Aibinu MO, Colin SC, Moyo S. Solving delay differ- Publishing. [CrossRef] ential equations via Sumudu transform. arXiv [Epub [18] Bokhari A. Application of Shehu transform to ahead of print]. doi: 10.22075/ijnaa.2021.22682.2402 Atangana-Baleanu derivatives. J Math Computer
6. Akgül A. A novel method for a fractional derivative Sci. 2019;20:101−107. [CrossRef] with non-local and non-singular kernel. Chaos Solit
7. Diethelm K, Ford J. Numerical solution of the Bagley- Fractals 2018;114:478−482. [CrossRef] Torvik equation. BIT Numerical Mathematics
8. Akgül EK, Akgül A, Yavuz M. New illustrative appli- cations of integral transforms to financial models 2002;42:490−507. [CrossRef] with different fractional derivatives. Chaos Solit [20] Ghanbari B, Atangana A. A new application of Fractals 2021;146:110877. [CrossRef] fractional Atangana-Baleanu derivatives: designing
9. Akgül EK, Akgül A, Alqahtani RT. A new applica- ABC-fractional masks in image processing. Phys A tion of the sumudu transform for the falling body Stat Mech Appl 2020;542:123516. [CrossRef] problem. J Funct Spaces 2021;2021:9702569. [CrossRef] [21] Gorenflo R, Kilbas AA, Mainardi F, Rogosin S.
10. Akgül EK, Jamshed W, Sooppy N, Elagan SK, Mittag-Leffler functions, related topics and applica- Alshehri NA. On solutions of gross domestic prod- tions. Berlin: Springer; 2014;Vol. 2. [CrossRef] uct model with different kernels. Alexandria Eng J [22] Haubold HJ, Mathai AM, Saxena S. Mittag-Leffler 2022;61:1289−1295. [CrossRef] functions and their applications. Journal of applied
11. Asiru MA. Sumudu transform and the solution of mathematics. 2011;2011:298628. [CrossRef] integral equations of convolution type. Int J Math [23] Kazem S. Exact solution of some linear fractional Educ Sci Technol 2001;32:906−910. [CrossRef] differential equations by Laplace transform. Int J
12. Aslam M, Farman M, Ahmad H, Gia TN, Ahmad Nonlinear Sci 2013;16:3−11. A, Askar S. Fractal fractional derivative on [24] Luchko Y, Gorenflo R. The initial value problem chemistry kinetics hires problem. AIMS Math for some fractional differential equations with the 2022;7:1155−1184. [CrossRef] Caputo derivatives.
13. Nanware JA, Patil NG. On Properties of Sumudu tem with Atangana-Baleanu derivatives with frac- Transform and Applications. Punjab University tional order. Chaos Solit Fractals 2016;89:447−454. Journal of Mathematics. 2021;53(9). [CrossRef]
14. Baleanu D, Fernandez A, Akgül A. On a fractional operator combining proportional and classical dif- of differential equations involving Caputo- ferintegrals. Mathematics 2020;8:360. [CrossRef] Fabrizio fractional operator and its applications
15. Belgacem FBM, Karaballi AA. Sumudu transform to reaction-diffusion equations. Adv Differ Equ fundamental properties investigations and applica- 2019;2019:178. [CrossRef] tions. Int J Stoch Anal 2006;2006:091083. [CrossRef] [27] Zada L, Aziz I. The numerical solution of frac-
16. Belgacem R, Baleanu D, Bokhari A. Shehu transform tional Korteweg‐de Vries and Burgers' equa- and applications to Caputo-fractional differential tions via Haar wavelet. Math Methods Appl Sci equations. Equations Int J Anal Appl 2019;17:917−927. 2021;44:10564−10577. [CrossRef]

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