Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2021, , 19 - 33, 31.12.2021
https://doi.org/10.54187/jnrs.974667

Öz

Kaynakça

  • M. R. Spiegel, Theory and problems of Laplace transform, McGraw Hill, New York, 1965.
  • S. Benzoni, Analyse de Fourier, Universite de Lyon, Lyon 1, Camille Jordan Institute, Saint-Étienne, 2011.
  • N. T. Negero, Zero-Order Hankel Transform Method for Partial Differential Equations, International Journal of Modern Science and Engineering Technology, 3(10), (2016) 24-36.
  • D. Lomen, Application of the Mellin Transforin to Boundary Value Problems, Proceedings of the Iowa Academy of Science, 69(1), (1962) 436-442.
  • G. K.Watugala, Sumudu transform: a new integral transform to solve differentia lequations and control engineering problems, International Journal of Mathematical Education in Science and Technology, 24(1), (1993) 35-43.
  • Z. H. Khan, W. A. Khan, N-transform properties and applications, NUST Journal of Engineering Sciences, 1, (2008) 127-133.
  • T.M. Elzaki, The New Integral Transform "ELzaki Transform", Global Journal of Pure and Applied Mathematics, 7(1), (2011) 57-64.
  • H. J. Kim, The time shifting theorem and the convolution for Elzaki transform, Global Journal of Pure and Applied Mathematics, 87, (2013) 261-271.
  • A. Devi, P. Roy, V. Gill, Solution of ordinary differential equations with variable coefficients using Elzaki transform, Asian Journal of Applied Science and Technology, 1, (2017) 186-194.
  • A. Kalavathi, T. Kohila, L. M. Upadhyaya, On the degenerate Elzaki transform, Bulletin of Pure and Applied Sciences Section -E-Mathematics & Statistics, 40E(1), (2021) 99-107.
  • K. S. Aboodh, The new integrale transform "Aboodh transform", Global Journal of Pure and Applied Mathematics, 9(1), (2013) 35-43.
  • Z. U. Zafar, ZZ Transform Method, International Journal of Advanced Engineering and Global Technoloy, 4(1), (2016) 1605-1611.
  • S. Maitama, W. Zhao, New Integral Transform: Shehu Transform a Generalization of Sumudu and Laplace Transform for Solving differential equations, International Journal of Analysis and Applications, 17(2), (2019) 167-190.
  • M. S. Archana, V. J. Pratibha, Elzaki Transform: A Solution of Differential Equations, International Journal of Scientific Engineering & Technology Research, 4(4), (2015) 1006-1008.
  • P. P. Chopade, S. B. Devi, Applications of Elzaki Transform to Ordinary Differential Equations and Partial Differential Equations, International Journal Advanced Research in Computer Science Software Engineering, 5(3), (2015) 38-41.
  • M. Eslaminasab, S. Abbasbandy, Study on usage of Elzaki transform for the ordinary differential equations with non-constant coefficients, International Journal of Industrial Mathematics, 7(3), (2015) 277-281.
  • T. M. Elzaki, S. M. Ezaki, On the ELzaki Transform and Ordinary Differential Equation with Variable Coefficients, Advances in Theoretical and Applied Mathematics, 6(1), (2011) 41-46.
  • T. M. Elzaki, S. M. Ezaki, On the ELzaki Transform and Higher Order Ordinary Differential Equations, Advances in Theoretical and Applied Mathematics, 6(1), (2011) 107-113.
  • T. M. Elzaki, S. M. Ezaki, Solution of Integro-Differential Equations by Using ELzaki Transform, Global Journal of Mathematical Sciences: Theory & Practical, 3(1), (2011) 1-11.
  • M. M. A. Mahgob, Elzaki Transform and a Bulge Function on Volterra Integral Equations of the Second Kind, IOSR Journal of Mathematics, 11(2), (2012) 68-70.
  • M. M. A. Mahgob, T.M. Elzaki, Solution of Partial Integro-Differential Equations by Elzaki Transform Method, Applied Mathematical Sciences, 9(6), (2015) 295-303.
  • M. M. A. Mahgob, T. M. Elzaki, Elzaki Transform and Integro-Differential Equation with a Bulge Function, IOSR Journal ofMathematics, 11(2), (2015) 25-28.
  • P. G. Bhadane, V. H. Pradhan, S. V. Desale, Elzaki Transform Solution of One Dimensional Ground Water Recharge through Spreading, International Journal of Engineering Research and Applications, 3(6), (2013) 1607-1610.
  • T.M. Elzaki, E. M. A.Hilal, Analytical Solution for Telegraph Equation by Modified of Sumudu Transform "Elzaki Transform", Mathematical Theory and Modeling, 2(4), (2012) 104-111.
  • T. M. Elzaki, S. M. Ezaki, On the ELzaki Transform and System of Partial Differential Equations, Advances in Theoretical and Applied Mathematics, 6(1), (2011) 115-123.
  • D. Ziane, M. Hamdi Cherif, Resolution of Nonlinear Partial Differential Equations by Elzaki Transform Decomposition Method, Journal of Approximation Theory and Applied Mathematics, 5, (2015) 17-30.
  • T. M. Elzaki, S. M. Elzaki, Applications of New Transform "ELzaki Transform" to Partial Differential Equations, Global Journal of Pure and Applied Mathematics, 7(1), (2011) 65-70.
  • A. Devi, M. Jakhar, Analytic solution of fractional order differential equation arising in RLC electrical circuit, Malaya Journal of Matematik, 8(2), (2020) 421-426.
  • D. Ziane, Application of Homotopy Analysis Method Combined with Elzaki Transform for Fractional Porous Medium Equation, Journal of Approximation Theory and Applied Mathematics, 6, (2019) 1-19.
  • D. Ziane, Elzaki transform and the decomposition method for nonlinear fractional partial differential equations, International Journal of Open Problems in Computer Science and Mathematics, 9(4), (2016) 25-39.
  • D. Ziane, M.Hamdi Cherif, K. Belghaba, Fractional higher dimensional initial boundary value problems via variational iteration method coupled with Elzaki transform, Nonlinear Studies, 24(4), (2017) 1-17.
  • D. Ziane, T. M. Elzaki, M. Hamdi Cherif, Elzaki transform combined with variational iteration method for partial differential equations of fractional order, Fundamental Journal of Mathematics and Applications, 1(1), (2018) 102-108.
  • H.M. Srivastava, A. K. Golmankhaneh, D. Baleanu, X. J. Yang, Local Fractional Sumudu Transform with Application to IVPs on Cantor Sets, Abstract and Applied Analysis, 2014, (2014) Article ID: 176395, 1-7.
  • X. J. Yang, Fractional Functional Analysis and Its Applications, Asian Academic, Hong Kong, 2011.
  • X. J. Yang, Local Fractional Calculus and Its Applications, World Scientific Publishing, New York, 2012.
  • J. H. He, Asymptotic Methods for Solitary Solutions and Compactons, Abstract and Applied Analysis, 2012, (2012) Article ID: 916793, 1-130.
  • C. G. Zhao, A. M. Yang, H. Jafari, A. Haghbin, The Yang-Laplace Transform for Solving the IVPs with Local Fractional Derivative, Abstract and Applied Analysis, 2014, Article ID: 386459, (2014) 1-5.
  • X. J. Yang, L. Li, R. Yang, Problems of local fractional definite integral of the one-variable nondifferentiable function,World Science and Technology R&D, 31(4), (2009) 722-724.
  • J. Ahmad, S. T. Mohyud-Din, H. M. Srivastava, X-J. Yang, Analytic solutions of the Helmholtz and Laplace equations by using local fractional derivative operators, Waves, Wavelets and Fractals – Advanced Analysis, 1, (2015) 22-26.
  • X. J. Yang, Generalized Sampling Theorem for Fractal Signals, Advances in Digital Multimedia, 1(2), (2012) 88-92.
  • G. Jumarie, Table of some basic fractional calculus formulae derived from a modified Riemann-Liouville derivative for non-differentiable functions, Applied Mathematics Letters, 22, (2009) 378-385.

Local fractional Elzaki transform and its application to local fractional differential equations

Yıl 2021, , 19 - 33, 31.12.2021
https://doi.org/10.54187/jnrs.974667

Öz

The objective of our work is to couple the Elzaki transform method and the local fractional derivative which is called local fractional Elzaki transform, where we have provided important results of this transformation as local fractional Laplace-Elzaki duality, Elzaki transform of the local fractional derivative and the local fractional integral and the local fractional convolution, also we have presented the properties of some special functions with the local fractional derivative sense. The Elzaki transform was applied to solve some linear local fractional differential equations in order to obtain non-differentiable analytical solutions. The results of the solved examples show the effectiveness of the proposed method.

Kaynakça

  • M. R. Spiegel, Theory and problems of Laplace transform, McGraw Hill, New York, 1965.
  • S. Benzoni, Analyse de Fourier, Universite de Lyon, Lyon 1, Camille Jordan Institute, Saint-Étienne, 2011.
  • N. T. Negero, Zero-Order Hankel Transform Method for Partial Differential Equations, International Journal of Modern Science and Engineering Technology, 3(10), (2016) 24-36.
  • D. Lomen, Application of the Mellin Transforin to Boundary Value Problems, Proceedings of the Iowa Academy of Science, 69(1), (1962) 436-442.
  • G. K.Watugala, Sumudu transform: a new integral transform to solve differentia lequations and control engineering problems, International Journal of Mathematical Education in Science and Technology, 24(1), (1993) 35-43.
  • Z. H. Khan, W. A. Khan, N-transform properties and applications, NUST Journal of Engineering Sciences, 1, (2008) 127-133.
  • T.M. Elzaki, The New Integral Transform "ELzaki Transform", Global Journal of Pure and Applied Mathematics, 7(1), (2011) 57-64.
  • H. J. Kim, The time shifting theorem and the convolution for Elzaki transform, Global Journal of Pure and Applied Mathematics, 87, (2013) 261-271.
  • A. Devi, P. Roy, V. Gill, Solution of ordinary differential equations with variable coefficients using Elzaki transform, Asian Journal of Applied Science and Technology, 1, (2017) 186-194.
  • A. Kalavathi, T. Kohila, L. M. Upadhyaya, On the degenerate Elzaki transform, Bulletin of Pure and Applied Sciences Section -E-Mathematics & Statistics, 40E(1), (2021) 99-107.
  • K. S. Aboodh, The new integrale transform "Aboodh transform", Global Journal of Pure and Applied Mathematics, 9(1), (2013) 35-43.
  • Z. U. Zafar, ZZ Transform Method, International Journal of Advanced Engineering and Global Technoloy, 4(1), (2016) 1605-1611.
  • S. Maitama, W. Zhao, New Integral Transform: Shehu Transform a Generalization of Sumudu and Laplace Transform for Solving differential equations, International Journal of Analysis and Applications, 17(2), (2019) 167-190.
  • M. S. Archana, V. J. Pratibha, Elzaki Transform: A Solution of Differential Equations, International Journal of Scientific Engineering & Technology Research, 4(4), (2015) 1006-1008.
  • P. P. Chopade, S. B. Devi, Applications of Elzaki Transform to Ordinary Differential Equations and Partial Differential Equations, International Journal Advanced Research in Computer Science Software Engineering, 5(3), (2015) 38-41.
  • M. Eslaminasab, S. Abbasbandy, Study on usage of Elzaki transform for the ordinary differential equations with non-constant coefficients, International Journal of Industrial Mathematics, 7(3), (2015) 277-281.
  • T. M. Elzaki, S. M. Ezaki, On the ELzaki Transform and Ordinary Differential Equation with Variable Coefficients, Advances in Theoretical and Applied Mathematics, 6(1), (2011) 41-46.
  • T. M. Elzaki, S. M. Ezaki, On the ELzaki Transform and Higher Order Ordinary Differential Equations, Advances in Theoretical and Applied Mathematics, 6(1), (2011) 107-113.
  • T. M. Elzaki, S. M. Ezaki, Solution of Integro-Differential Equations by Using ELzaki Transform, Global Journal of Mathematical Sciences: Theory & Practical, 3(1), (2011) 1-11.
  • M. M. A. Mahgob, Elzaki Transform and a Bulge Function on Volterra Integral Equations of the Second Kind, IOSR Journal of Mathematics, 11(2), (2012) 68-70.
  • M. M. A. Mahgob, T.M. Elzaki, Solution of Partial Integro-Differential Equations by Elzaki Transform Method, Applied Mathematical Sciences, 9(6), (2015) 295-303.
  • M. M. A. Mahgob, T. M. Elzaki, Elzaki Transform and Integro-Differential Equation with a Bulge Function, IOSR Journal ofMathematics, 11(2), (2015) 25-28.
  • P. G. Bhadane, V. H. Pradhan, S. V. Desale, Elzaki Transform Solution of One Dimensional Ground Water Recharge through Spreading, International Journal of Engineering Research and Applications, 3(6), (2013) 1607-1610.
  • T.M. Elzaki, E. M. A.Hilal, Analytical Solution for Telegraph Equation by Modified of Sumudu Transform "Elzaki Transform", Mathematical Theory and Modeling, 2(4), (2012) 104-111.
  • T. M. Elzaki, S. M. Ezaki, On the ELzaki Transform and System of Partial Differential Equations, Advances in Theoretical and Applied Mathematics, 6(1), (2011) 115-123.
  • D. Ziane, M. Hamdi Cherif, Resolution of Nonlinear Partial Differential Equations by Elzaki Transform Decomposition Method, Journal of Approximation Theory and Applied Mathematics, 5, (2015) 17-30.
  • T. M. Elzaki, S. M. Elzaki, Applications of New Transform "ELzaki Transform" to Partial Differential Equations, Global Journal of Pure and Applied Mathematics, 7(1), (2011) 65-70.
  • A. Devi, M. Jakhar, Analytic solution of fractional order differential equation arising in RLC electrical circuit, Malaya Journal of Matematik, 8(2), (2020) 421-426.
  • D. Ziane, Application of Homotopy Analysis Method Combined with Elzaki Transform for Fractional Porous Medium Equation, Journal of Approximation Theory and Applied Mathematics, 6, (2019) 1-19.
  • D. Ziane, Elzaki transform and the decomposition method for nonlinear fractional partial differential equations, International Journal of Open Problems in Computer Science and Mathematics, 9(4), (2016) 25-39.
  • D. Ziane, M.Hamdi Cherif, K. Belghaba, Fractional higher dimensional initial boundary value problems via variational iteration method coupled with Elzaki transform, Nonlinear Studies, 24(4), (2017) 1-17.
  • D. Ziane, T. M. Elzaki, M. Hamdi Cherif, Elzaki transform combined with variational iteration method for partial differential equations of fractional order, Fundamental Journal of Mathematics and Applications, 1(1), (2018) 102-108.
  • H.M. Srivastava, A. K. Golmankhaneh, D. Baleanu, X. J. Yang, Local Fractional Sumudu Transform with Application to IVPs on Cantor Sets, Abstract and Applied Analysis, 2014, (2014) Article ID: 176395, 1-7.
  • X. J. Yang, Fractional Functional Analysis and Its Applications, Asian Academic, Hong Kong, 2011.
  • X. J. Yang, Local Fractional Calculus and Its Applications, World Scientific Publishing, New York, 2012.
  • J. H. He, Asymptotic Methods for Solitary Solutions and Compactons, Abstract and Applied Analysis, 2012, (2012) Article ID: 916793, 1-130.
  • C. G. Zhao, A. M. Yang, H. Jafari, A. Haghbin, The Yang-Laplace Transform for Solving the IVPs with Local Fractional Derivative, Abstract and Applied Analysis, 2014, Article ID: 386459, (2014) 1-5.
  • X. J. Yang, L. Li, R. Yang, Problems of local fractional definite integral of the one-variable nondifferentiable function,World Science and Technology R&D, 31(4), (2009) 722-724.
  • J. Ahmad, S. T. Mohyud-Din, H. M. Srivastava, X-J. Yang, Analytic solutions of the Helmholtz and Laplace equations by using local fractional derivative operators, Waves, Wavelets and Fractals – Advanced Analysis, 1, (2015) 22-26.
  • X. J. Yang, Generalized Sampling Theorem for Fractal Signals, Advances in Digital Multimedia, 1(2), (2012) 88-92.
  • G. Jumarie, Table of some basic fractional calculus formulae derived from a modified Riemann-Liouville derivative for non-differentiable functions, Applied Mathematics Letters, 22, (2009) 378-385.
Toplam 41 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Uygulamalı Matematik
Bölüm Articles
Yazarlar

Djelloul Ziane 0000-0002-1941-2633

Mountassir Hamdi Cherif 0000-0003-3458-1918

Yayımlanma Tarihi 31 Aralık 2021
Yayımlandığı Sayı Yıl 2021

Kaynak Göster

APA Ziane, D., & Hamdi Cherif, M. (2021). Local fractional Elzaki transform and its application to local fractional differential equations. Journal of New Results in Science, 10(3), 19-33. https://doi.org/10.54187/jnrs.974667
AMA Ziane D, Hamdi Cherif M. Local fractional Elzaki transform and its application to local fractional differential equations. JNRS. Aralık 2021;10(3):19-33. doi:10.54187/jnrs.974667
Chicago Ziane, Djelloul, ve Mountassir Hamdi Cherif. “Local Fractional Elzaki Transform and Its Application to Local Fractional Differential Equations”. Journal of New Results in Science 10, sy. 3 (Aralık 2021): 19-33. https://doi.org/10.54187/jnrs.974667.
EndNote Ziane D, Hamdi Cherif M (01 Aralık 2021) Local fractional Elzaki transform and its application to local fractional differential equations. Journal of New Results in Science 10 3 19–33.
IEEE D. Ziane ve M. Hamdi Cherif, “Local fractional Elzaki transform and its application to local fractional differential equations”, JNRS, c. 10, sy. 3, ss. 19–33, 2021, doi: 10.54187/jnrs.974667.
ISNAD Ziane, Djelloul - Hamdi Cherif, Mountassir. “Local Fractional Elzaki Transform and Its Application to Local Fractional Differential Equations”. Journal of New Results in Science 10/3 (Aralık 2021), 19-33. https://doi.org/10.54187/jnrs.974667.
JAMA Ziane D, Hamdi Cherif M. Local fractional Elzaki transform and its application to local fractional differential equations. JNRS. 2021;10:19–33.
MLA Ziane, Djelloul ve Mountassir Hamdi Cherif. “Local Fractional Elzaki Transform and Its Application to Local Fractional Differential Equations”. Journal of New Results in Science, c. 10, sy. 3, 2021, ss. 19-33, doi:10.54187/jnrs.974667.
Vancouver Ziane D, Hamdi Cherif M. Local fractional Elzaki transform and its application to local fractional differential equations. JNRS. 2021;10(3):19-33.


TR Dizin 31688

EBSCO30456


Electronic Journals Library EZB   30356

 DOAJ   30355                                             

WorldCat  30357                                             303573035530355

Academindex   30358

SOBİAD   30359

Scilit   30360


29388 As of 2021, JNRS is licensed under a Creative Commons Attribution-NonCommercial 4.0 International Licence (CC BY-NC).