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Title
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Solving Distributed-Order Fractional Equations via Genocchi Wavelets and Weighted Residual Method.
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Type
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JournalPaper
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Keywords
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کلیدواژهها: Distributed-order fractional differential equations, Fractional in tegral operator, Beta function, Collocation method, Genocchi wavelets.
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Abstract
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خلاصه: In this work, a novel method to finding the numerical solution of distributed order fractional differential equations (DFDEs) is introduced. This method is based on the Genocchi wavelets (GWs), and weighted residual method (collocations method). For this aim, an exact mathematical formula that in corporates regularized beta functions is meticulously formulated to ascertain the Riemann-Liouville fractional integral operator (R-LFIO) corresponding to these specific wavelets. By employing the aforementioned integral opera tor and leveraging the capabilities of Gauss-Legendre numerical integration, the original problem is adeptly transformed into a comprehensive system of algebraic equations, thereby facilitating a more manageable analysis and solution process. Also, the error analysis is investigated and examples are given to demonstrate the effectiveness and accuracy of the method.
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Researchers
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Reza Moeti (Third Researcher), Elham Keshavarz (Second Researcher), Parisa Rahimkhani (First Researcher)
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