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In this paper, we derive a new generalized integral transform on Dzherbashian-Nersesian fractional operator and give some special cases. We make a generalization of the application of integral transformations to different fractional operators, where several previous results can be invoked from a single relation. We also use the new results obtained to solve some fractional differential equations involving the recent revival of Dzherbashian-Nersesian fractional operators. [ABSTRACT FROM AUTHOR]

The basic idea of the present study is to apply the local fractional Sumudu decomposition method (LFSDM) presented in [31] to solve Lane-Emden of index m and Emden-Fowler equation of index m with local fractional derivative, in order to obtain non differentiable analytical solutions. The results of the solved local differential fractional equations show the effectiveness of this method. [ABSTRACT FROM AUTHOR]

Prabhakar fractional operator was applied recently for studying the dynamics of complex systems from several branches of sciences and engineering. In this manuscript, we discuss the regularized Prabhakar derivative applied to fractional partial differential equations using the Sumudu homotopy analysis method(PSHAM). Three illustrative examples are investigated to confirm our main results. [ABSTRACT FROM AUTHOR]

We investigate through this research the numerical inversion technique for the Laplace transforms cooperated by the integration Boubaker polynomials operational matrix. The efficiency of the presented approach is demonstrated by solving some differential equations. Also, this technique is combined with the standard Laplace Homotopy Perturbation Method. The numerical results highlight that there is a very good agreement between the estimated solutions with exact solutions. [ABSTRACT FROM AUTHOR]

The basic motivation of the present study is to apply the local fractional homotopy analysis method (HAM) to solve the coupled nonlinear system of Burger's equations with local fractional derivative. The derivatives operators are taken in the local fractional sense. The result obtained through the proposed system, proves the effectiveness of this method (LFHAM) in dealing with these types of problems, which is confirmed in relation to other works. [ABSTRACT FROM AUTHOR]