ARTICLE | doi:10.20944/preprints202103.0148.v1
Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Adomian decomposition method; variational iteration method; Volterra-Fredholm integro-differential equation; approximate solution.
Online: 4 March 2021 (09:20:22 CET)
In this article, we present a comparative study between the Adomian Decomposition Method (ADM) and Variational Iteration Method (VIM). The study outlines the significant features of the two methods, for solving nonlinear Volterra-Fredholm integro-differential equations. From the computational viewpoint, the VIM is more efficient, convenient and easy to use. Moreover, we proved the existence and uniqueness results and convergence of the solution. Finally, an example is included to demonstrate the validity and applicability of the proposed techniques.
ARTICLE | doi:10.20944/preprints202102.0517.v1
Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Impulsive fractional differential inclusions; Nonlocal conditions; Fixed point theorems; 10 Mild solutions
Online: 23 February 2021 (14:16:13 CET)
In this article, we are interested in a new generic class of nonlocal fractional impulsive differential inclusions with linear sectorial operator and Lipschitz multivalued function in the setting of finite dimensional Banach spaces. By modifying the definition of PC-mild solutions initiated by Shu, we succeeded to determine new conditions that sufficiently guarantee the existence of the solutions. The results are obtained by combining techniques of fractional calculus and fixed point theorem for contraction maps. We also characterize the topological structure of the set of solutions. Finally, we provide a demonstration to address the applicability of the theoretical results.