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.
Highlights
In recent years, fractional calculus is considered to be a fascinating field of research, due to the wide applications of fractional integrals and derivatives in mathematical modeling of systems and processes in many fields of engineering and science [1,2,3,4,5,6,7,8,9,10,11,12,13]
We can refer to fractional Homotopy Perturbation [14], fractional Adomian decomposition [15], Yang-Laplace transform [16], Variational Iteration and function decomposition in local fractional sense [15,17]
Homotopy Perturbation coupled with Sumudu transform technique is an integration between two powerful methods: Sumudu transform, which was proposed by Watugala [18] in 1993, and Homotopy perturbation, which was introduced by He [19,20]
Summary
Fractional calculus is considered to be a fascinating field of research, due to the wide applications of fractional integrals and derivatives in mathematical modeling of systems and processes in many fields of engineering and science [1,2,3,4,5,6,7,8,9,10,11,12,13]. Homotopy Perturbation coupled with Sumudu transform technique is an integration between two powerful methods: Sumudu transform, which was proposed by Watugala [18] in 1993, and Homotopy perturbation, which was introduced by He [19,20] This combined method was applied to solve fractional nonlinear problems, arising in the field of nonlinear sciences such as engineering and mathematical physics. Several researchers used this simple tool to obtain solutions of nonlinear differential equations. The aim of this paper is to implement the combination of local fractional Sumudu transform and homotopy perturbation in order to get analytical solutions of some local fractional problems in mathematical physics, for example dissipative and damped wave equations.
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