Maan A.  Rasheed, Mustafa A.  Sabri, 
    Deriving the General Laplace Inversion Formula using Complex Integration
Results and its Applications in Solving Partial Differential Equations,
    Journal of Engineering and Applied Sciences,
    Volume 14,Issue 10,
    2019,
    Pages 3455-3462,
    ISSN 1816-949x,
    jeasci.2019.3455.3462,
    (https://makhillpublications.co/view-article.php?doi=jeasci.2019.3455.3462)
    Abstract: This study is concerned with Laplace transform and its applications to partial differential equations. We derive the general Laplace inversion formula using some complex analysis results. Furthermore, we apply
this formula to find the formal solution of a heat conduction problem which is heat equation with Neumann boundary conditions. We conclude that Laplace transforms with the inversion formula provide a potent
technique for solving partial differential equations.
    Keywords: Laplace transform;inversion formula;heat conduction;Cauchy integral formula;Neumann
boundary conditions;equations