Solution of Fractional Telegraph Equations by Conformable Double Convolution Laplace Transform

Waleed M. Osman, Tarig M. Elzaki, Nagat A. A. Siddig


This paper covers both conformable double Laplace transform and conformable double convolution, including their definitions, theorems and properties. The purpose of this research is to solve a fresh case of fractional telegraph equations with conformable double convolution by conformable double Laplace transform.


Conformable double Laplace transform; Fractional telegraph equation; Conformable double convolution

Full Text:



T. Abdeljawad, On conformable fractional calculus, Journal of Computational and Applied Mathematics 279 (2015), 57 – 66, DOI: 10.1016/

A. Atangana, D. Baleanu and A. Alsaedi, New properties of conformable derivative, Open Mathematics 13 (2015), 889 – 898, DOI: 10.1515/math-2015-0081.

A. Babakhani and R. S. Dahiya, Systems of multi-dimensional Laplace transform and heat equation, in 16th Conference on Applied Mathematics, University of Central Oklahoma, Electronic Journal of Differential Equations, Conf. 07 (2001), 25 – 36, URL:

R. R. Dhunde and G. L. Waghmare, On some convergence theorems of double laplace transform, Journal of Informatics and Mathematical Sciences 6(1) (2014), 45 – 54, DOI: 10.26713/jims.v6i1.242.

H. EltayebGadain, Application of double Laplace decomposition method for solving singular one dimensional system of hyperbolic equations, Journal of Nonlinear Sciences and Applications 10 (2017), 111 – 121, DOI: 10.22436/jnsa.010.01.11.

T. M. Elzaki and E. M. A. Hilal, Solution of telegraph equation by modified of double Sumudu transform “Elzaki Transform”, Mathematical Theory and Modeling 2(4) (2012), 95 – 103, URL:

T. M. Elzaki and J. Biazar, Homotopy perturbation method and elzaki transform for solving system of nonlinear partial differential equations, World Applied Sciences Journal 24(7) (2013), 944 – 948, DOI: 10.5829/idosi.wasj.2013.24.07.1041.

T. M. Elzaki, Application of projected differential transform method on nonlinear partial differential equations with proportional delay in one variable, World Applied Sciences Journal 30(3) (2014), 345 – 349, DOI: 10.5829/idosi.wasj.2014.30.03.1841.

T. M. Elzaki, Double Laplace variational iteration method for solution of nonlinear convolution partial differential equations, Archives Des Sciences 65(12) (2012), 588 – 593, URL:

R. Jiwari, S. Pandit and R. C. Mittal, A differential quadrature algorithm for the numerical solution of the second-order one dimensional hyperbolic telegraph equation, International Journal of Nonlinear Science 13(3) (2012), 259 – 266, URL:

R. Jiwari, S. Pandit and R. C. Mittal, A differential quadrature algorithm to solve the two dimensional linear hyperbolic telegraph equation with Diriclet and Neumann boundary conditions, Applied Mathematics and Computation 218 (2012), 7279 – 7294, DOI: 10.1016/j.amc.2012.01.006.

H. Eltayeb, I. Bachar and M. Gad-Allah, Solution of singular one-dimensional Boussinesq equation by using double conformable Laplace decomposition method, Advances in Difference Equations 2019 (2019), Article number: 293, DOI: 10.1186/s13662-019-2230-1.

R. Khalil, M. Al Horani, A. Yousef and M. Sababheh, A new definition of fractional derivative, Journal of Computational and Applied Mathematics 264 (2014), 65 – 70, DOI: 10.1016/

A. Korkmaz and K. Hosseini, Exact solutions of a nonlinear conformable time-fractional parabolic equation with exponential nonlinearity using reliable methods, Optical and Quantum Electronics 49 (2017), Article number: 278, DOI: 10.1007/s11082-017-1116-2.

A. Korkmaz, On the wave solutions of conformable fractional evolution equations, Communications Faculty of Sciences University of Ankara Series A1 67(1) (2018), 68 – 79, DOI: 10.1501/Commua1_0000000831.

O. Özkan and A. Kurt, On conformable double Laplace transform, Optical and Quantum Electronics 50 (2018), Article number: 103, DOI: 10.1007/s11082-018-1372-9.

A. Prakash, P. Veeresha, D. G. Prakasha and M. Goyal, A homotopy technique for a fractional order multi-dimensional telegraph equation via the Laplace transform, The European Physical Journal Plus 134 (2019), Article number: 19, 1 – 18, URL:

G. C. Wu, Laplace transform overcoming principle drawbacks in application of the variational iteration method to fractional heat equations, Thermal Science 16(4) (2012), 1257 – 1261, URL:



  • There are currently no refbacks.

eISSN 0975-8607; pISSN 0976-5905