In this paper, we introduce a new resolvent operator and we call it relaxed resolvent operator. We prove that relaxed resolvent operator is single-valued and Lipschitz continuous and finally we approximate the solution of a variational inclusion problem in Hilbert spaces by defining an iterative algorithm based on relaxed resolvent operator. A few concepts like Lipschitz continuity and strong m...

We will prove that we can specialize the indeterminate α in a linear differential α-resolvent of a univariate polynomial over a differential field of characteristic zero to an integer q to obtain a q-resolvent. We use this idea to obtain a formula, known as the powersum formula, for the terms of theα-resolvent. Finally, we use the powersum formula to rediscover Cockle’s differential resolvent o...

This work develops scattering and spectral analysis of a discrete impulsive Sturm-Liouville equation with parameter in boundary condition. Giving the Jost solution solutions this problem, we find function problem. Discussing properties function, solutions, asymptotic behavior solution, Green resolvent operator, continuous point spectrum Finally, give an example which main results are made expli...

In this paper we present a numerical method for fuzzy differential equation of fractional order under gH-fractional Caputo differentiability. The main idea of this method is to approximate the solution of fuzzy fractional differential equation (FFDE) by an implicit method as corrector and explicit method as predictor. This method is tested on numerical examples.

In this paper, Adomian decomposition method (ADM) and homotopy analysis method (HAM) are proposed to solving the fuzzy nonlinear Volterra-Fredholm integral equation of the second kind(FV FIE− 2). we convert a fuzzy nonlinear Volterra-Fredholm integral equation to a nonlinear system of Volterra-Fredholm integral equation in crisp case. we use ADM , HAM and find the approximate solution of this s...

Multi-dimensional Fuzzy differential equations driven by multi-dimensional Liu process, have been intensively applied in many fields. However, we can not obtain the analytic solution of every multi-dimensional fuzzy differential equation. Then, it is necessary for us to discuss the numerical results in most situations. This paper focuses on the numerical method of multi-dimensional fuzzy differ...

In this paper an alternative approach to solve uncertain Stochastic Differential Equation (SDE) is proposed. This uncertainty occurs due to the involved parameters in system and these are considered as Triangular Fuzzy Numbers (TFN). Here the proposed fuzzy arithmetic in [2] is used as a tool to handle Fuzzy Stochastic Differential Equation (FSDE). In particular, a system of Ito stochastic diff...

Fractional Fornberg-Whitham equation has a vast application in physics. There exist various investigations for the above problem by considering the variables and parameters as crisp/exact. In practice, we may not have these parameters exactly but those may be known in some uncertain form. In the present paper, these uncertainties are taken as interval/fuzzy and the authors proposed here a new m...

In this paper, we use the generalized differentiability concept tostudy the fuzzy transport equation. We consider transport equationin the homogeneous and non-homogeneous cases with fuzzy initialcondition. We also present the solution when speed parameter is a fuzzynumber. Our method is based on the construction of the solutionsby employing Zadeh's extension principle.