scholarly journals Analytical solutions of fractional wave equation with memory effect using the fractional derivative with exponential kernel

2021 ◽  
pp. 104148
Author(s):  
B. Cuahutenango-Barro ◽  
M.A. Taneco-Hernández ◽  
J.F. Gómez-Aguilar ◽  
M.S. Osman ◽  
Hadi Jahanshahi ◽  
...  
2018 ◽  
Vol 115 ◽  
pp. 283-299 ◽  
Author(s):  
B. Cuahutenango-Barro ◽  
M.A. Taneco-Hernández ◽  
J.F. Gómez-Aguilar

Fluids ◽  
2021 ◽  
Vol 6 (7) ◽  
pp. 235
Author(s):  
Chen Yue ◽  
Dianchen Lu ◽  
Mostafa M. A. Khater

This research paper targets the fractional Hirota’s analytical solutions–Satsuma (HS) equations. The conformable fractional derivative is employed to convert the fractional system into a system with an integer–order. The extended simplest equation (ESE) and modified Kudryashov (MKud) methods are used to construct novel solutions of the considered model. The solutions’ accuracy is investigated by handling the computational solutions with the Adomian decomposition method. The solutions are explained in some different sketches to demonstrate more novel properties of the considered model.


2021 ◽  
Vol 11 (9) ◽  
pp. 4142
Author(s):  
Nehad Ali Shah ◽  
Abdul Rauf ◽  
Dumitru Vieru ◽  
Kanokwan Sitthithakerngkiet ◽  
Poom Kumam

A generalized mathematical model of the radial groundwater flow to or from a well is studied using the time-fractional derivative with Mittag-Lefler kernel. Two temporal orders of fractional derivatives which characterize small and large pores are considered in the fractional diffusion–wave equation. New analytical solutions to the distributed-order fractional diffusion–wave equation are determined using the Laplace and Dirichlet-Weber integral transforms. The influence of the fractional parameters on the radial groundwater flow is analyzed by numerical calculations and graphical illustrations are obtained with the software Mathcad.


2012 ◽  
Vol E95-C (3) ◽  
pp. 382-394
Author(s):  
Yasuyuki OISHI ◽  
Shigekazu KIMURA ◽  
Eisuke FUKUDA ◽  
Takeshi TAKANO ◽  
Daisuke TAKAGO ◽  
...  

2021 ◽  
pp. 104017
Author(s):  
Supriya Yadav ◽  
Devendra Kumar ◽  
Jagdev Singh ◽  
Dumitru Baleanu

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Ming-Sheng Hu ◽  
Ravi P. Agarwal ◽  
Xiao-Jun Yang

We introduce the wave equation in fractal vibrating string in the framework of the local fractional calculus. Our particular attention is devoted to the technique of the local fractional Fourier series for processing these local fractional differential operators in a way accessible to applied scientists. By applying this technique we derive the local fractional Fourier series solution of the local fractional wave equation in fractal vibrating string and show the fundamental role of the Mittag-Leffler function.


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