On solving Caputo and Riemann–Liouville types of sequential fractional differential equations with boundary conditions using an accurate scheme

Due to its significance in every branch of science and engineering today, it is crucial to solve sequential fractional differential equations (SFDEs). In this research work, we study some unique theories on fractional calculus. We present significant relationships among well-known fractional derivative operators and leverage these relationships to create novel approaches to the solution of linear sequential fractional differential equations (LSFDE) with constant coefficients. We use a reliable technique called the Adomian decomposition natural method (ADNM), which combines Adomian decomposition and the natural transform method. The ADNM was then modified to find exact and approximate solutions to fractional partial differential equations (FPDEs) with boundary conditions (B.C.s). The study demonstrates the effectiveness of this technique since it is convenient to implement and provides accurate results. This comprehensive method provides valuable knowledge for scholars and scientists in the science and engineering fields.