Implementation and Convergence Analysis of Homotopy Perturbation Coupled With Sumudu Transform to Construct Solutions of Local-Fractional PDEs

Abstract

Abstract:In the present paper, the explicit solutions of some local fractional partial differential equations are constructed through the integration of local fractional Sumudu transform and homotopy perturbation such as local fractional dissipative and damped wave equations. The convergence aspect of this technique is also discussed and presented. The obtained results prove that the employed method is very simple and effective for treating analytically various kinds of problems comprising local fractional derivatives.

Solution of Ambartsumian Delay Differential Equation with Conformable Derivative

“…The convergence of the Homotopy perturbation method (HPM) was discussed in detail for ODEs (ordinary differential equations) by Ayati and Biazar [23]. For FPDEs (fractional partial differential equations), the convergence of the HPM was recently analyzed by Touchent et al [34] and Sene and Fall [33]. Ayati and Biazar [23] proved that the series in Equation (28) is convergent in the limit if ∃ (0…”

A new fractal nonlinear Burgers' equation arising in the acoustic signals propagation

“…13,14 The fractal acoustic wave equation was discussed in Ray. 15 The fractal damped wave equation was considered in Ait Touchent et al 16 The fractal Klein-Gordon equation was proposed in Kumar et al 17 The fractal-time-space wave equation was presented in Hemeda et al 18 The fractal Laplace equation was investigated in Ziane et al 19 The fractal finite-dimensional heat-conduction equation was proposed in Debbouche and Antonov. 20 The travelling-wave transformation of nondifferentiable type was given to solve the fractal Korteweg-de Vries equation.…”

Laplace decomposition for solving nonlinear system of fractional order partial differential equations

“…In the last decade, scientists and engineers have paid much attention towards nonlinear equations, as the nonlinearity exists everywhere in most of the physical problems. The nonlinear partial differential equations of fractional order (FPDEs) are the special case of nonlinear equations that have many applications in science and technology, including chemistry, biology, physics, vibration, acoustic, signals processing, electromagnetic, polymeric materials, and fluid dynamics, super conductivity, optics, and quantum mechanics [1][2][3][4]. Due to frequent appearance of FPDEs in different disciplines of engineering and science, the researchers have added a lot of research contribution to both theory of mathematical science and technology [5][6][7][8][9].…”