Analysis of time‐fractional fuzzy vibration equation of large membranes using double parametric based Residual power series method

Abstract

The study of the time‐fractional vibration equation (VE) of large membranes is vital due to its widespread applications. Various researchers have investigated the titled problem in which the variables and parameters have been considered as crisp/exact. However, in actual practice, this may contain uncertainty because of errors in observations, maintenance induced error, and other errors. In this investigation, we have considered these uncertainties as interval/fuzzy, and a method, namely double parametric form of fuzzy numbers are used to solve the uncertain fractional vibration model of order α(1<α≤2). The titled problem has been solved under various cases using the Residual power series method (RPSM). The performance of the present method is well in terms of computational efficiency. The consistency of the method is displayed by providing numerical solutions for various cases. Obtained results are depicted in terms of figures and are also compared with individual cases.

Numerical simulation of a class of space fractional bistable systems based on the Fourier spectral method

“…In this section, we give the Turing bifurcation conditions of system (1). We assume the equilibrium point of the nondiffusive system (1) is E * = (u 0 , v 0 ), so…”

“…Fractional partial differential equations are becoming widely used as a suitable modeling approach for many fields in science and engineering. [1][2][3][4][5][6] We mainly study models arising in the application areas of theoretical biology, physics, and chemistry, modeled by some space fractional bistable systems…”

A Semianalytical Approach for the Solution of Nonlinear Modified Camassa–Holm Equation with Fractional Order

“…Integral transform methods are extremely e ective in reducing the complexity of these nonlinear fractional problems. ere are a number of popular and effective schemes to tackle the nonlinear appearance of these models with fractional order such as the Laplace transform [6], Fourier series approach [7], F-Expansion scheme [8], Residual power series method [9], (G /G)-expansion approach [10], Trial equation approach [11], Sinc-Bernoulli collocation method [12], Variational iteration scheme [13], Subequation [14], Homotopy perturbation method [15], spline collocation approach [16], and so on.…”

Fuzzy Fractional Order Volterra-Fredholm Integro-Differential Equations Using MADM

“…The article "A novel coronavirus infection system using a FFDE under Caputo's sense" by S. Ahmad and others may be found in [19]. To solve systems of FFDEs with fuzzy initial conditions under fuzzy Caputo differentiability (CD), Chakraverty et al investigated time fractional fuzzy vibration equation of large membranes using double parametric based residual power series method in [20]. The concept of fuzziness is addressed in [21] using various fractional equations [22].…”