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A new recursive scheme for solving a fractional differential equation of ray tracing through the crystalline lens

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Abstract

The goal of this work is to solve an initial-value problem for a fractional differential equation that governs the ray tracing through a crystalline lens using an interesting variation of the Adomian decomposition method. A new recursive scheme is presented by combining the Adomian decomposition method with a formula and via the solutions of the well-known generalized Abel equation. It is shown that the technique  used here offers advantages in computing the components \(y_{n}, n=1,2,\ldots\) in an easily computed formula.

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Author notes

  1. Bougoffa Lazhar and Wazwaz Abdul-Majid have contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics, LTM, University of Batna 2, Mostefa Ben Boulaïd, Fesdis, 05078, Batna, Algeria

    Abdelaziz Mennouni

  2. Faculty of Science, Department of Mathematics, Imam Mohammad Ibn Saud Islamic University, P.O. Box 90950, Riyadh, 11623, Saudi Arabia

    Lazhar Bougoffa

  3. Department of Mathematics, Saint Xavier University, Chicago, IL, 60655, USA

    Abdul-Majid Wazwaz

Authors
  1. Abdelaziz Mennouni
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  2. Lazhar Bougoffa
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  3. Abdul-Majid Wazwaz
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Correspondence to Abdelaziz Mennouni.

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Mennouni, A., Bougoffa, L. & Wazwaz, AM. A new recursive scheme for solving a fractional differential equation of ray tracing through the crystalline lens. Opt Quant Electron 54, 373 (2022). https://doi.org/10.1007/s11082-022-03766-w

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