Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2023, Cilt: 41 Sayı: 6, 1132 - 1143, 29.12.2023

Öz

Kaynakça

  • 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.

Application of the sumudu transform to some equations with fractional derivatives

Yıl 2023, Cilt: 41 Sayı: 6, 1132 - 1143, 29.12.2023

Öz

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.

Kaynakça

  • 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.
Toplam 28 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Klinik Kimya
Bölüm Research Articles
Yazarlar

Ali Akgül 0000-0001-9832-1424

Gamze Öztürk 0000-0001-9046-8288

Yayımlanma Tarihi 29 Aralık 2023
Gönderilme Tarihi 11 Ekim 2021
Yayımlandığı Sayı Yıl 2023 Cilt: 41 Sayı: 6

Kaynak Göster

Vancouver Akgül A, Öztürk G. Application of the sumudu transform to some equations with fractional derivatives. SIGMA. 2023;41(6):1132-43.

IMPORTANT NOTE: JOURNAL SUBMISSION LINK https://eds.yildiz.edu.tr/sigma/