Analysis of imprecisely defined fuzzy space-fractional telegraph equations
- PDF / 1,671,899 Bytes
- 10 Pages / 595.276 x 790.866 pts Page_size
- 91 Downloads / 213 Views
© Indian Academy of Sciences
Analysis of imprecisely defined fuzzy space-fractional telegraph equations SMITA TAPASWINI1 and DIPTIRANJAN BEHERA2,∗ 1 Department
of Mathematics, Government Autonomous College, Angul 759 143, India of Mathematics, The University of the West Indies, Mona Campus, Kingston 7, Jamaica ∗ Corresponding author. E-mail: [email protected]; [email protected] 2 Department
MS received 17 August 2019; accepted 1 October 2019 Abstract. Telegraph equations are very important in physics and engineering due to their importance in modelling and designing frequency or voltage transmission. Moreover, uncertainty present in the system parameters plays a vital role in the designing process. Also it is known that it is not always easy to find exact solution of fractionally ordered system. Taking these factors into consideration, here space-fractional telegraph equations with fuzzy uncertainty have been analysed. A new technique to represent fuzzy number using two different parameters in the same domain has been used along with a semianalytic approach known as Adomain decomposition method (ADM) for the solution. Gaussian and triangular shaped fuzzy numbers are considered to model the uncertainties in initial as well as boundary conditions. The obtained results are compared with the existing solution in special cases for the validation. Keywords. Fuzzy space-fractional telegraph equations; triangular and Gaussian fuzzy numbers; Adomain decomposition method. PACS Nos 02.60.Cb; 02.70.−c; 02.30.Jr; 02.90.+p
1. Introduction Telegraph equations have great significance in areas of physics [1,2], mathematics [3–5], wave propagation [6], signal analysis [7], random walk theory [8] and other disciplines. These are used to produce and design high frequency and voltage transmission lines. In particular, fractional space telegraph equation has been analysed explicitly in [9–20]. Neville et al [9] obtained numerical solution of fractional telegraph equation using finite difference method and also established its stability. Orsingher and Zhao [11] studied the same type of problem and obtained the Fourier transform of the obtained solution. Adomain decomposition method (ADM) is used by Momani [10] to obtain the solution of space and time-fractional telegraph problem. Same type of problem has been solved by Ahmad and Ibrahim [12] using the method of separation of variables. Zhao and Li [13] used difference method and finite element method to find the approximate solution of the space–time fractional telegraph equation. A new perturbative Laplace method has been developed by Khan 0123456789().: V,-vol
et al [14] for solving space–time fractional telegraph equations. Garg et al [15] implemented transform method to obtain the solution of space–time fractional telegraph equation. The homotopy perturbation method has successfully been incorporated by Yıldırım [16] to obtain an approximate solution. Sevimlican [17] used variational iteration method (VIM) for the solution of governing equation. Ford et al [18
Data Loading...
