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.

Fokker–Planck equation with interval and fuzzy uncertainty has been considered in this paper. Also the derivatives involved with respect to time and space are assumed to be fractional in nature. This problem has been solved using variational iteration method (VIM) along with the double parametric form of fuzzy numbers. For the analysis, both triangular and Gaussian normalised fuzzy sets are taken into consideration. Numerical results for different cases have been obtained and those are depicted in terms of plots and are also compared in special cases for the validation. Moreover, using an important method known as successive approximation method, it has also been verified that the obtained solutions are the same as that of VIM as both methods are equivalent.

In this paper, we have studied analytical travelling wave solution of a non-linear fifth-order time fractional Korteweg–De Vries (KdV) equation under the conformal fractional derivative. This equation is very important as it has many applications in various fields such as fluid dynamics, plasma physics, shallow water waves etc. Also, most importantly, the considered fractional-order derivative plays a vital role as it can be varied to obtain different waves. Here, a new form of exact travelling wave solution is derived using the powerful sine–cosine method. To understand the physical phenomena, some visual representations of the solution by varying different parameters are given. Accordingly, it has been observed that the obtained wave solutions are solitons in nature. Also,from the results, one can conclude that the corresponding wave of the solution will translate from left to right by increasing the fractional order α. Furthermore, extending the range of x it can be noticed that there is a reduction inthe heights of the waves. Also similar observations have been made for a particular time interval and by increasing the values of x. Also, it can be observed that the present method is straightforward as well as computationally efficient compared to the existing methods. The obtained solution has been verified using Maple software and the results are validated.