Numerical and analytical approach to the Chandrasekhar quadratic functional integral equation using Picard and Adomian decomposition methods

Eman A. A. Ziada; Hind Hashem; Asma Al-Jaser; Osama Moaaz; Monica Botros; Eman A. A. Ziada; Hind Hashem; Asma Al-Jaser; Osama Moaaz; Monica Botros

doi:10.3934/era.2024275

Electronic Research Archive

2024, Volume 32, Issue 11: 5943-5965. doi: 10.3934/era.2024275

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Numerical and analytical approach to the Chandrasekhar quadratic functional integral equation using Picard and Adomian decomposition methods

1.
Basic Science Department, Nile Higher Institute for Engineering and Technology, Mansoura, Egypt
2.
Faculty of Science, Alexandria University, Egypt
3.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
4.
Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia
5.
Basic Science Department, Faculty of Engineering, Delta University for Science and Technology, Gamasa 11152, Egypt
6.
Faculty of Artificial Intelligence, Delta University for Science and Technology, Gamasa 11152, Egypt

Received: 19 July 2024 Revised: 12 October 2024 Accepted: 24 October 2024 Published: 05 November 2024

This research aimed to find numerical solutions to a type of nonlinear initial value problem (IVP) for hybrid fractional differential equations. Using the Adomian decomposition method (ADM) and the Picard method (PM), we studied the Chandrasekhar quadratic integral equation (QIE). Furthermore, we investigated existence and uniqueness results using measures of weak noncompactness. Through a set of examples and numerical simulations, a comparison was made between the results of the AMD and PM.
- hybrid integral equation,
- measure of noncompactness,
- Adomian decomposition method,
- Picard method,
- fractional derivatives
Citation: Eman A. A. Ziada, Hind Hashem, Asma Al-Jaser, Osama Moaaz, Monica Botros. Numerical and analytical approach to the Chandrasekhar quadratic functional integral equation using Picard and Adomian decomposition methods[J]. Electronic Research Archive, 2024, 32(11): 5943-5965. doi: 10.3934/era.2024275

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Abstract

This research aimed to find numerical solutions to a type of nonlinear initial value problem (IVP) for hybrid fractional differential equations. Using the Adomian decomposition method (ADM) and the Picard method (PM), we studied the Chandrasekhar quadratic integral equation (QIE). Furthermore, we investigated existence and uniqueness results using measures of weak noncompactness. Through a set of examples and numerical simulations, a comparison was made between the results of the AMD and PM.

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