In this research study, a novel computational algorithm for solving second-order singular functional differential equation as generalization of the well-known Lane–Emden and differential-difference equations is presented by using Bessel bases. This technique depends on transforming problem into system algebraic unknown coefficients are determined solution will be known. The method tested severa...

In the present paper, the analytical solution for an exact second order fuzzy initial value problem under generalized Hukuhara differentiability is obtained. First the solution of first order linear fuzzy differential equation under generalized Hukuhara differentiability is investigated using integration factor methods in two cases. The second based on the type of generalized Hukuhara different...

Uncertain differential equation with jumps is a type of differential equation driven by two classes of uncertain processes, namely canonical process and renewal process. Based on uncertain differential equation with jumps, this paper proposes a stock model with jumps for uncertain financial markets. Furthermore, the European call and put option pricing formulas for the stock model are formulate...

In this paper we consider the nonlinear parabolic integro-differential equation with initial and boundary conditions. We develop the method of generalized quasilinearization to generate linear iterates that converge quadratically to the unique solution of the nonlinear parabolic integro-differential equation. For this purpose, we establish comparison results for the parabolic integro-differenti...

In this paper, we study the Hyers-Ulam stability with respect to linear differential condition of fourth order. Specifically, treat ${\psi}$ as an interact arrangement condition, i.e., $ \begin{align*} {\psi}^{iv} ({\varkappa}) + {\xi}_1 {\psi}{'''} ({\varkappa})+ {\xi}_2 {\psi}{''} {\xi}_3 {\psi}' {\xi}_4 {\psi}({\varkappa}) = {\Psi}({\varkappa}) \end{align*} $ where ${\psi} \in c^...

The symmetry group method is applied to a generalized Korteweg-de Vries equation and several classes of group invariant solutions for it are obtained by means of this technique. Polynomial, trigonometric, and elliptic function solutions can be calculated. It is shown that this generalized equation can be reduced to a first-order equation under a particular second-order differential constraint w...