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Initial Value Problems with Generalized Fractional Derivatives and Their Solutions via Generalized Laplace Decomposition Method

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  • Mohamed Elbadri

Abstract

In this article, we use the p‐Laplace decomposition method to find the solution to the initial value problems that involve generalized fractional derivatives. The p‐Laplace decomposition method is used to get approximate series solutions. The Adomian decomposition is improved with the assistance of the p‐Laplace transform to examine the solutions of the given examples to demonstrate the precision of the current technique.

Suggested Citation

  • Mohamed Elbadri, 2022. "Initial Value Problems with Generalized Fractional Derivatives and Their Solutions via Generalized Laplace Decomposition Method," Advances in Mathematical Physics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jnlamp:v:2022:y:2022:i:1:n:3586802
    DOI: 10.1155/2022/3586802
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    References listed on IDEAS

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    1. Owyed, Saud & Abdou, M.A. & Abdel-Aty, Abdel-Haleem & Alharbi, W. & Nekhili, Ramzi, 2020. "Numerical and approximate solutions for coupled time fractional nonlinear evolutions equations via reduced differential transform method," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    2. Mohamed Elbadri & Shams A. Ahmed & Yahya T. Abdalla & Walid Hdidi, 2020. "A New Solution of Time-Fractional Coupled KdV Equation by Using Natural Decomposition Method," Abstract and Applied Analysis, Hindawi, vol. 2020, pages 1-9, September.
    3. Mohamed Elbadri & Shams A. Ahmed & Yahya T. Abdalla & Walid Hdidi, 2020. "A New Solution of Time‐Fractional Coupled KdV Equation by Using Natural Decomposition Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2020(1).
    4. Akgül, Esra Karatas & Akgül, Ali & Yavuz, Mehmet, 2021. "New Illustrative Applications of Integral Transforms to Financial Models with Different Fractional Derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
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