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Some Analytical Techniques in Fractional Calculus: Realities and Challenges

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Discontinuity and Complexity in Nonlinear Physical Systems

Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 6))

Abstract

In the last decades, much effort has been dedicated to analytical aspects of the fractional differential equations. The Adomian decomposition method and the variational iteration method have been developed from ordinary calculus and become two frequently used analytical methods. In this article, the recent developments of the methods in the fractional calculus are reviewed. The realities and challenges are comprehensively encompassed.

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Acknowledgments

This work was partly supported by the National Natural Science Foundation of China (No. 11171295, No. 11061028) and the key program (51134018).

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Sciences, Cankaya University, 06530, Balgat, Ankara, Turkey

    Dumitru Baleanu

  2. Institute of Space Sciences, Magurele-Bucharest, Romania

    Dumitru Baleanu

  3. Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia

    Dumitru Baleanu

  4. College of Mathematics and Information Science, Neijiang Normal University, 641112, Neijiang, P.R. China

    Guo-Cheng Wu

  5. School of Mathematics and Information Sciences, Zhaoqing University, Zhaoqing, Guang Dong, 526061, P.R. China

    Jun-Sheng Duan

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  1. Dumitru Baleanu
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  2. Guo-Cheng Wu
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  3. Jun-Sheng Duan
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Correspondence to Dumitru Baleanu .

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Editors and Affiliations

  1. Department of Electrical Engineering, Polytechnic Institute of Porto Institute of Engineering, Porto, Portugal

    J. A. Tenreiro Machado

  2. Faculty of Art and Sciences, Mathematics and Computer Sciences, Cankaya University, Ankara, Turkey

    Dumitru Baleanu

  3. Department of Mechanical Engineering, Southern Illinois University Edwardsville, Edwardsville, Illinois, USA

    Albert C J Luo

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Baleanu, D., Wu, GC., Duan, JS. (2014). Some Analytical Techniques in Fractional Calculus: Realities and Challenges. In: Machado, J., Baleanu, D., Luo, A. (eds) Discontinuity and Complexity in Nonlinear Physical Systems. Nonlinear Systems and Complexity, vol 6. Springer, Cham. https://doi.org/10.1007/978-3-319-01411-1_3

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