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A New Attractive Analytic Approach for Solutions of Linear and Nonlinear Neutral Fractional Pantograph Equations

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  • Eriqat, Tareq
  • El-Ajou, Ahmad
  • Oqielat, Moa'ath N.
  • Al-Zhour, Zeyad
  • Momani, Shaher

Abstract

In this paper, we present analytical solutions for linear and nonlinear neutral Caputo-fractional pantograph differential equations. An attractive new method we called the Laplace-Residual power series method, is introduced and used to create series solutions for the target equations. This method is an efficient simple technique for finding exact and approximate series solutions to the linear and nonlinear neutral fractional differential equations. In addition, numerical and graphical results are also addressed at different values of α to show the behaviors of the Laplace-Residual power series solutions compared with other methods such as Two-stage order-one Runge-Kutta, one-legθ, variational iterative, Chebyshev polynomials, Laguerre wavelet, Bernoulli wavelet, Boubaker polynomials, Hermit wavelet, Proposed and Pricewise fractional-order Taylor methods. Finally, several examples are also considered and solved based on this method to show that our new approach is simple, accurate, and applicable. Maple software is used to calculate the numerical and symbolic quantities in the paper.

Suggested Citation

  • Eriqat, Tareq & El-Ajou, Ahmad & Oqielat, Moa'ath N. & Al-Zhour, Zeyad & Momani, Shaher, 2020. "A New Attractive Analytic Approach for Solutions of Linear and Nonlinear Neutral Fractional Pantograph Equations," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    • Handle: RePEc:eee:chsofr:v:138:y:2020:i:c:s0960077920303568
    DOI: 10.1016/j.chaos.2020.109957
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    References listed on IDEAS

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    1. Arikoglu, Aytac & Ozkol, Ibrahim, 2007. "Solution of fractional differential equations by using differential transform method," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1473-1481.
    2. Bellen, Alfredo & Zennaro, Marino, 2003. "Numerical Methods for Delay Differential Equations," OUP Catalogue, Oxford University Press, number 9780198506546, Decembrie.
    3. Abdulnasir Isah & Chang Phang & Piau Phang, 2017. "Collocation Method Based on Genocchi Operational Matrix for Solving Generalized Fractional Pantograph Equations," International Journal of Differential Equations, Hindawi, vol. 2017, pages 1-10, June.
    4. Momani, Shaher, 2006. "Non-perturbative analytical solutions of the space- and time-fractional Burgers equations," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 930-937.
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