TY - JOUR AU - Aghili, Arman PY - 2022/12/31 Y2 - 2024/03/28 TI - Direct methods for singular integral equations and non-homogeneous parabolic PDEs JF - J. Numer. Anal. Approx. Theory JA - J. Numer. Anal. Approx. Theory VL - 51 IS - 2 SE - Articles DO - 10.33993/jnaat512-1269 UR - https://ictp.acad.ro/jnaat/journal/article/view/1269 SP - 109-123 AB - <p><span class="fontstyle0">In this article, the author presented some applications of the Laplace, \(</span><span class="fontstyle2">L^</span><span class="fontstyle3">2\)</span><span class="fontstyle0">, and Post-Widder transforms for solving fractional Singular Integral Equations, impulsive differential equation and systems of differential equations. Finally, analytic solution for a non-homogeneous partial differential equation with non-constant coefficients is given. </span><span class="fontstyle0">The obtained results reveal that the integral transform method is an effective tool and convenient.</span></p> ER -