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In the context of fractal space, this study presents a higher-order nonlinear local fractional Bratu-type equation and thoroughly examines this generalized nonlinear equation. Additional analysis and identification of particular special situations of the generalized local fractional Bratu equation is performed. Finally, the Adomian decomposition method is utilized to derive that solution for the generalized Bratu equation of local fractional type. This study contributes to a deeper understanding of these equations and provides a practical computational approach to their solutions.