Development and Application of Mamadu Integral Transforms to Differential Calculus

Integral transforms such as the Elzaki, Aboodh, Sumudu, Natural, Sawi, and Shehu transforms have been developed to tackle some complex differential equations through the substantial advancements in the application of integral transforms. To seek the improvement of convergence, stability, and accuracy when solving differential equations, the Mamadu transform is developed and implemented. The Mamadu transform is an essential analytical tool built using a well-known kernel function that incorporates a polynomial and exponential-based terms. A major advantage of the Mamadu transform is the inclusion of a weight function to improve long-term behavior and singularities in differential equations. The method involves reducing a complex differential equation to an algebraic expression, making solution derivation and manipulation simpler. Also, the method offers a well-structured and efficient problem solving. Three examples are considered to illustrate the effectiveness and effectiveness of the Mamadu transform in the solution of different differential equations. Comparing with other traditional methods shows increased accuracy, faster convergence, and higher stability. The method is equally helpful in terms of computational efficiency and accuracy for the solution of fractional calculus, where other methods fail. Furthermore, the study reflects the relevance of Mamadu transform as a renowned analytical technique in applied sciences, particularly in fields such as mathematical modeling and engineering.