Application of the sumudu transform to some equations with fractional derivatives

Year 2023, Volume: 41 Issue: 6, 1132 - 1143, 29.12.2023

Ali Akgül , Gamze Öztürk

Abstract

The aim of the article is to obtain the exact solutions of the linear fractional differential equations by the integral transforms. Exact solutions of the equations with power-law, exponential-decay and Mittag-Leffler kernels have been obtained by the Sumudu transform. We demonstrate some simulations to show the effect of the proposed transforms.

Keywords

Fractional Differential Equations , Sumudu Transform , Inverse Sumudu Transform

References

• 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.
• [2] Ahmed SA. Applications of New Double Integral Transform (Laplace–Sumudu Transform) in Mathematical Physics. In Abstract and Applied Analysis. 2021;2021. Hindawi.
• [3] Al-Humedi HO, Kadhim SAH. Solution of linear fuzzy fractional differential equations using fuzzy natural transform. Earthline J Math Sci 2022;8:4165.
• [4] Aibinu MO, Moyo SC, Moyo S. Analyzing population dynamics models via Sumudu transform. arXiv [Epub ahead of print]. doi: 10.48550/arXiv.2112.07126
• [5] Aibinu MO, Colin SC, Moyo S. Solving delay differential equations via Sumudu transform. arXiv [Epub ahead of print]. doi: 10.22075/ijnaa.2021.22682.2402
• [6] Akgül A. A novel method for a fractional derivative with non-local and non-singular kernel. Chaos Solit Fractals 2018;114:478482.
• [7] Akgül EK, Akgül A, Yavuz M. New illustrative applications of integral transforms to financial models with different fractional derivatives. Chaos Solit Fractals 2021;146:110877.
• [8] Akgül EK, Akgül A, Alqahtani RT. A new application of the sumudu transform for the falling body problem. J Funct Spaces 2021;2021:9702569.
• [9] Akgül EK, Jamshed W, Sooppy N, Elagan SK, Alshehri NA. On solutions of gross domestic product model with different kernels. Alexandria Eng J 2022;61:12891295.
• [10] Asiru MA. Sumudu transform and the solution of integral equations of convolution type. Int J Math Educ Sci Technol 2001;32:906910.
• [11] Aslam M, Farman M, Ahmad H, Gia TN, Ahmad A, Askar S. Fractal fractional derivative on chemistry kinetics hires problem. AIMS Math 2022;7:11551184.
• [12] Atangana A, Koca I. Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order. Chaos Solit Fractals 2016;89:447454.
• [13] Baleanu D, Fernandez A, Akgül A. On a fractional operator combining proportional and classical differintegrals. Mathematics 2020;8:360.
• [14] Belgacem FBM, Karaballi AA. Sumudu transform fundamental properties investigations and applications. Int J Stoch Anal 2006;2006:091083.
• [15] Belgacem R, Baleanu D, Bokhari A. Shehu transform and applications to Caputo-fractional differential equations. Equations Int J Anal Appl 2019;17:917927.
• [16] Belgacem FBM, Karaballi AA, et al. Analytical investigations of the Sumudu transform and applications to integral production equations. Math Problems Eng 2003;2003:103118.
• [17] Bhargava A, Jain RK, et al. A Comparative Study of Laplace Transform and Sumudu Transform on-Function. In IOP Conference Series: Materials Science and Engineering. 2021;1099(1):012024. IOP Publishing.
• [18] Bokhari A. Application of Shehu transform to Atangana-Baleanu derivatives. J Math Computer Sci. 2019;20:101107.
• [19] Diethelm K, Ford J. Numerical solution of the Bagley-Torvik equation. BIT Numerical Mathematics 2002;42:490507.
• [20] Ghanbari B, Atangana A. A new application of fractional Atangana–Baleanu derivatives: designing ABC-fractional masks in image processing. Phys A Stat Mech Appl 2020;542:123516.
• [21] Gorenflo R, Kilbas AA, Mainardi F, Rogosin S. Mittag-Leffler functions, related topics and applications. Berlin: Springer; 2014;Vol. 2.
• [22] Haubold HJ, Mathai AM, Saxena S. Mittag-Leffler functions and their applications. Journal of applied mathematics. 2011;2011:298628.
• [23] Kazem S. Exact solution of some linear fractional differential equations by Laplace transform. Int J Nonlinear Sci 2013;16:311.
• [24] Luchko Y, Gorenflo R. The initial value problem for some fractional differential equations with the Caputo derivatives.
• [25] Nanware JA, Patil NG. On Properties of Sumudu Transform and Applications. Punjab University Journal of Mathematics. 2021;53(9).
• [26] Shaikh A, Tassaddiq A, Nisar KS, Baleanu Analysis of differential equations involving Caputo–Fabrizio fractional operator and its applications to reaction–diffusion equations. Adv Differ Equ 2019;2019:178.
• [27] Zada L, Aziz I. The numerical solution of fractional Korteweg‐de Vries and Burgers' equations via Haar wavelet. Math Methods Appl Sci 2021;44:1056410577.