Boundary value problems (BVPs) constitute a fundamental class of differential equations where the solutions are determined by prescribing values at the boundaries of the domain. The study of positive ...

Fourth-order boundary value problems (BVPs) constitute an essential class of differential equations where the highest derivative is of fourth order. These equations arise naturally in the mathematical ...

Fourier series solutions are obtained for mixed boundary value problems for the Laplace equation in the plane and in the sphere. The nature of the boundary conditions presents difficulties in ...

Reviews ordinary differential equations, including solutions by Fourier series. Physical derivation of the classical linear partial differential equations (heat, wave, and Laplace equations). Solution ...

The focus of this study is on boundary-value issues for Caputo-type fractional differential equations of order 1 < q < 2. To begin, we demonstrate the existence theorem of mild solutions under certain ...