Initial Value Problems with Generalized Fractional Derivatives and Their Solutions via Generalized Laplace Decomposition Method
Mohamed Elbadri
Abstract
In this article, we use the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"><a:mi mathvariant="script">p</a:mi></a:math> -Laplace decomposition method to find the solution to the initial value problems that involve generalized fractional derivatives. The <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" id="M2"><d:mi mathvariant="script">p</d:mi></d:math> -Laplace decomposition method is used to get approximate series solutions. The Adomian decomposition is improved with the assistance of the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" id="M3"><g:mi mathvariant="script">p</g:mi></g:math> -Laplace transform to examine the solutions of the given examples to demonstrate the precision of the current technique.