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Description
This work examines the solution of fractional integro-differential equations using the Adomian decomposition method, utilizing a unique kernel operator. The fractional term is specified in the Caputo framework, and the solution is derived by an approximate and analytical method. The fixed-point theorems are employed to establish the existence and uniqueness of the solution. Further, the stability of the solution is discussed by applying the definition of Ulam-Hyers (U-H) stability types. A thorough investigation of error analysis is conducted to evaluate the precision of the methodologies, with results obtained through tested instances demonstrated. The analytical method is surprisingly efficient and straightforward, delivering a precise solution in a single iteration. Comparisons with alternative approaches, illustrated by error tables and graphs, indicate which method is more effective regarding processing time and cost regarding numerical and analytical methods. The proposed method effectively solves fractional order differential equations and is pertinent to various scientific issues.
