f5b994c2-fa0f-4800-9485-27bc97cf255620210518023227100naun:naunmdt@crossref.orgMDT DepositInternational Journal of Circuits, Systems and Signal Processing1998-446410.46300/9106http://www.naun.org/cms.action?id=3029118202111820211510.46300/9106.2021.15https://naun.org/cms.action?id=23283Discrete (G'/G )-expansion: a Method Used to Get Exact Solution of Fdde (Fractional Differential-difference Equation) Linked With Nltl (Non-linear Transmission Line)SuchanaMishraEEE Department, Dayananda Sagar College of Engineering, Bangalore-560078, Karnataka, INDIARabindraKishore MishraElectronics Department, Bhanja Bihar, Bramhapur -760007, Odisha, INDIASrikantaPatnaikCSE Department, Siksha O Anusandhan University, Bhubaneswar-751030, Odisha, INDIAHere, we have used the discrete (G'/G)-expansion procedure with the derivative operator MR-L (modified Riemann-Liouville) and FCT (fractional complex transform) to find the exact/analytical solution of an electrical transmission line which is non-linear. Results include solutions for integer and fractional DDE. We consider two special cases of solutions: hyperbolic and trigonometric. Hyperbolic solutions indicate propagation of singular wave on the transmission line. Trigonometric solutions show propagation of complex wave.51820215182021453460https://www.naun.org/main/NAUN/circuitssystemssignal/2021/a982005-049(2021).pdf10.46300/9106.2021.15.49https://www.naun.org/main/NAUN/circuitssystemssignal/2021/a982005-049(2021).pdfK. B. Oldham and J. Spanier, ―The Fractional Calculus‖, Academic Press, New York, 1974. Suchana Mishra, Rabindra Kishore Mishra, Srikant Patnaik, ―some applications of fractional calculus in technological development―,Journal of Fractional Calculus and Application, ISSN: 2090-5858, Volume 10, Issue 1, pp. 228-235, January 2019. Suchana Mishra, Rabindra Kishore Mishra, Srikant Patnaik, ―Fractional Cross Product in Radiation Characteristic of Micro-strip Antenna: A simulation Approach‖, Test engineering and management, ISSN: 0193-4120, Volume 81, pp. 1392-1401, Publication Issue November-December 2019. 10.1016/j.camwa.2010.02.018A. Saadatmandi and M. Dehghan, ―Numerical solution of the higherorder linear Fredholm integro-differential-difference equation with variable coefficients‖, Computer and Mathematics with Applications, Volume 59, Issue 8, pp. 2996-3004, April 2010. 10.1088/0031-8949/78/01/015013C.Q. Dai and Y.Y. Wang, ―Exact travelling wave solutions of the discrete nonlinear Schrödinger equation and the hybrid lattice equation obtained via the exp-function method‖, Physica Scripta, The Royal Swedish Academy of Sciences, Volume 78, Number 1, 2 July 2008. 10.1016/j.cpc.2009.01.010Z. Wang, ―Discrete tanh method for nonlinear difference-differential equations‖, Computer Physics Communications, Volume 180, Issue 7, pp. 1104- 1108, July 2009. 10.1515/zna-2011-1-206S. Zhang, Y.N. Sun, J.M. Ba, and L. Dong, ‖The Modified (G'/G)- Expansion Method for Nonlinear Evolution Equations‖, Zeitschrift für Naturforschung A, Volume 66, Issue 1-2, pp. 33-39 , 2011. E. Fermi, J. Pasta, and S. Ulam, ―Collected Papers of Enrico Fermi‖, Volume 2, University of Chicago Press, Chicago, 1965. 10.1143/jpsj.60.2095Y. Ohta and R. Hirota, ‖A Discrete KdV Equation and Its Casorati Determinant Solution‖, Journal of the Physical Society of Japan, Volume 60, pp. 2095, 1991. 10.1007/978-3-642-83219-2_6Toda M., ―Recent Advances in the Theory of Nonlinear Lattices‖, Theory of Nonlinear Lattices, Springer Series in Solid-State Sciences, vol 20. Springer, Berlin, Heidelberg, pp. 159-176, 1989. 10.37394/232016.2020.15.24Vishnu Charan T., Alivelu Ìanga Parimi, Chandram Karri, ―Installation Cost Estimation of IPFC for Power Loss Reduction in Transmission Lines using Firefly Algorithm‖, WSEAS Transactions on Power Systems, ISSN / E-ISSN: 1790-5060 / 2224-350X, Volume 15, Art. #24, pp. 206-213, 2020. 10.37394/232016.2020.15.7Abdullah M. Shaheen, Ragab A. El-Sehiemy, ―Binary and Integer Coded Backtracking Search Optimization Algorithm for Transmission Network Expansion Planning‖, WSEAS Transactions on Power Systems, ISSN / E-ISSN: 1790-5060 / 2224-350X, Volume 14, Art. #6, pp. 47-54, 2019. 10.1088/1674-1056/23/12/120506S. Abdoulkary, A. Mohamadou, O. Dafounansou, and S.Y. Doka,‖ Exact solutions of the nonlinear differential-difference equations associated with the nonlinear electrical transmission line through a variable-coefficient discrete (G'/G)-expansion method‖, Chinese Physical Society and IOP Publishing Ltd, Chinese Physics B, Volume 23, Number 12, pp. 120506-1-7, October 2014. 10.1088/0253-6102/66/3/315Ismail Aslan, ―Exact Solutions for a Local Fractional DDE Associated with a Nonlinear Transmission Line‖, Communications in Theoretical Physics, Volume 66, Number 3, pp 315-320, September 2016. 10.1140/epjp/i2018-11851-1Emmanuel Fendzi-Donfack, Jean Pierre Nguenang and Laurent Nana, ―Fractional analysis for nonlinear electrical transmission line schroedinger equation with incomplete sub-equation‖, The European Physical Journal Plus 133, 32, 2018.