Bell wavelet-based numerical algorithm for fractional-order (1+1)-dimensional telegraph equations involving derivative in Caputo sense
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Date
2025
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Abstract
This study presents an efficient numerical approach for solving fractional-order (1+1)-dimensional telegraph equations using
a collocation method based on Bell wavelets. The method begins by exploring the fundamental properties of Bell polynomials
and their associated wavelets. Fractional-order operational matrices of integrals (OMI) are developed using block-pulse
functions, and the Bell wavelet OMI is then combined with collocation points to transform the telegraph equation into a
system of algebraic equations. Newton’s iterative technique is used to solve these equations. To validate the effectiveness and
applicability of the proposed Bell wavelet method, several test problems are analyzed, with detailed error analysis included.
Comparative results between the Bell wavelet approximate solutions and those from other established methods in the existing
literature are presented through comprehensive figures and tables. This comparison highlights the improved accuracy and
efficiency of the Bell wavelet method, demonstrating its potential as a reliable tool for solving fractional telegraph equations.
Keywords Bell polynomials · Bell wavelets · Fractional telegraph equation · Error analysis · Collocation points · Operational
matrix