Application of generalized differential transform method to multi-order fractional differential equations |
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| Authors: | Vedat Suat Erturk Shaher Momani Zaid Odibat |
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| Affiliation: | aDepartment of Mathematics, Faculty of Arts and Sciences, Ondokuz Mayis University, 55139, Kurupelit, Samsun, Turkey;bDepartment of Mathematics and Physics, Faculty of Arts and Sciences, Qatar University, Qatar;cPrince Abdullah Bin Ghazi Faculty of Science and IT, Al-Balqa’ Applied University, Salt, Jordan |
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| Abstract: | In a recent paper [Odibat Z, Momani S, Erturk VS. Generalized differential transform method: application to differential equations of fractional order, Appl Math Comput. submitted for publication] the authors presented a new generalization of the differential transform method that would extended the application of the method to differential equations of fractional order. In this paper, an application of the new technique is applied to solve fractional differential equations of the form y(μ)(t)=f(t,y(t),y(β1)(t),y(β2)(t),…,y(βn)(t)) with μ>βn>βn-1>…>β1>0, combined with suitable initial conditions. The fractional derivatives are understood in the Caputo sense. The method provides the solution in the form of a rapidly convergent series. Numerical examples are used to illustrate the preciseness and effectiveness of the new generalization. |
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| Keywords: | Fractional differential equations Differential transform method Multi-order equations Caputo fractional derivative |
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