Convergence of collocation Bernoulli wavelet method in solving nonlinear Fredholm integro-differential equations of fractional order

Subject Areas : Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering

Abdolali Rooholahi ¹ , Saeed Akhavan ²

1 - a Department of Mathematics, Lorestan university, Khorramabad, Iran
2 - Department of Mathematics, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr/Isfahan, Iran

Received: 2023-01-15 Accepted : 2023-05-27 Published : 2024-02-15

Keywords: Fractional calculus, Bernoulli wavelets, Fredholm integro-differential equations, collocation method.,

Abstract :

We provide a computer method for solving fractional order nonlinear Fredholm integro-differential equations in this study. This method transforms the core issue into a set of algebraic equations using Bernoulli wavelets. The operational Bernoulli wavelet with fractional integration is obtained and used. It works particularly well for technical applications. The convergence of the suggested strategy is the most crucial aspect to note here. The collocation approach for this issue has a unique approximation since these requirements can be shown using mathematical principles and matrices theory. Finally, some pertinent examples for which the exact solution is known are used in numerical simulation to confirm the effectiveness and relevance. Alternatively, these examples will demonstrate the viability and correctness of the suggested approach. We provide a computer method for solving fractional order nonlinear Fredholm integro-differential equations in this study. This method transforms the core issue into a set of algebraic equations using Bernoulli wavelets. The operational Bernoulli wavelet with fractional integration is obtained and used. It works particularly well for technical applications. The convergence of the suggested strategy is the most crucial aspect to note here. The collocation approach for this issue has a unique approximation since these requirements can be shown using mathematical principles and matrices theory. Finally, some pertinent examples for which the exact solution is known are used in numerical simulation to confirm the effectiveness and relevance. Alternatively, these examples will demonstrate the viability and correctness of the suggested approach.

References:


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