In this paper, We interpret a fuzzy differential equation by using the strongly generalized differentiability concept. Utilizing the Generalized characterization Theorem. Then a novel hybrid method based on learning algorithm of fuzzy neural network for the solution of differential equation with fuzzy initial value is presented. Here neural network is considered as a part of large field called ...

In this paper, a novel hybrid method based on learning algorithmof fuzzy neural network and Newton-Cotesmethods with positive coefficient for the solution of linear Fredholm integro-differential equation of the second kindwith fuzzy initial value is presented. Here neural network isconsidered as a part of large field called neural computing orsoft computing. We propose alearning algorithm from ...

In this paper we use the fuzzy Caputo derivatives under generalized Hukuhara difference to introduce fuzzy fractional Volterra-Fredholm integro-differential equations and prove the existence and uniqueness of the solutions for this class of fractional equations.

In this paper,  The Picard method is proposed to solve the system of first-order fuzzy  differential equations  $(FDEs)$ with fuzzy initial conditions under generalized $H$-differentiability. Theexistence and uniqueness of the solution and convergence of theproposed method are proved in details. Finally, the method is illustrated by solving some examples.

In this paper we apply hybrid functions of general block-pulse‎ ‎functions and Legendre polynomials for solving linear and‎ ‎nonlinear multi-order fractional differential equations (FDEs)‎. ‎Our approach is based on incorporating operational matrices of‎ ‎FDEs with hybrid functions that reduces the FDEs problems to‎ ‎the solution of algebraic systems‎. ‎Error estimate that verifies a‎ ‎converge...

In this paper, we consider fuzzy fractional partial differential equations under Caputo generalized Hukuhara differentiability. Some new results on the existence and uniqueness of two types of fuzzy solutions are studied via  weakly contractive mapping in the partially ordered metric space. Some application examples are presented to illustrate our main results.

We are concerned with the development of a K−step method for the numerical solution of fuzzy initial value problems. Convergence and stability of the method are also proved in detail. Moreover, a specific method of order 4 is found. The numerical results show that the proposed fourth order method is efficient for solving fuzzy differential equations.

In this paper‎, ‎first‎, ‎a numerical method is presented for solving a class of linear Fredholm integro-differential equation‎. ‎The operational matrix of derivative is obtained by introducing hybrid third kind Chebyshev polynomials and Block-pulse functions‎. ‎The application of the proposed operational matrix with tau method is then utilized to transform the integro-differential equations to...

mathematical models can simulate the growth and proliferation of cells in the interaction with healthy cells, the immune system and measure the toxicity of drug and its effects on healthy tissue pay. one of the main goals of modeling the structure and growth of cancer cells is to find a control model suitable for administration among patients. in this study, a new mathematical model is designed...