Novel solution methods for initial boundary value problems of fractional order with conformable differentiation

By Mehmet Yavuz. 2017

73 citations recorded by the source corpus.

In this work, we develop a formulation for the approximate-analytical solution of fractional partial differential equations (PDEs) by using conformable fractional derivative. Firstly, we redefine the conformable fractional Adomian decomposition method (CFADM) and conformable fractional modified homotopy perturbation method (CFMHPM). Then, we solve some initial boundary value problems (IBVP) by using the proposed methods, which can analytically solve the fractional partial differential equations (FPDE). In order to show the efficiencies of these methods, we have compared the numerical and exact solutions of the IBVP. Also, we have found out that the proposed models are very efficient and powerful techniques in finding approximate solutions for the IBVP of fractional order in the conformable sense.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/1518d4352bc2fc2547d96f993c0e2a0cd28c842c

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In Applied Mathematics

1. Mehmet Yavuz
2. Necati Özdemir
3. Ndolane Sene

In Modeling and Simulation

1. Mehmet Yavuz
2. Necati Özdemir
3. Ndolane Sene

In Numerical Analysis

1. Mehmet Yavuz
2. Necati Özdemir
3. Ndolane Sene

Citations in the corpus

• European Vanilla Option Pricing Model of Fractional Order without Singular Kernel (2018, methodology): “For example, these techniques have been used to evaluate the performance of an electrical resistance inductance and capacitance (RLC) circuit using a new fractional operator with a local and nonlocal kernel [1], to price fractional European vanilla-type options [2,3], to analyze a new model of H1N1 ”