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An efficient method to solve a fractional differential equation by using linear programming and its application to an optimal control problem
This paper presents a new idea to solve fractional differential equations and fractional optimal control problems. The fractional derivative is defined in the Grunwald–Letnikov sense. The method is based on the linear programming problem...
Solving differential equations of fractional order using an optimization technique based on training artificial neural network
The current study aims to approximate the solution of fractional differential equations (FDEs) by using the fundamental properties of artificial neural networks (ANNs) for function approximation. In the first step, we derive an approximate solution...
Numerical solutions for solving a class of fractional optimal control problems via fixed-point approach
In this paper, an optimization problem is performed to obtain an approximate solution for a class of fractional optimal control problems (FOCPs) with the initial and final conditions. The main characteristic of our ...
Existence, uniqueness and stability of fuzzy fractional differential equations with local Lipschitz and linear growth conditions
Fuzzy fractional differential equations (FFDEs) driven by Liu’s process are a type of
fractional differential equations. In this paper, we intend to provide and prove a novel
existence and uniqueness theorem for the solutions of FFDEs...
An Analytical and Approximate Solution for Nonlinear Volterra Partial Integro-Differential Equations with a Weakly Singular Kernel Using the Fractional Differential Transform Method
An analytical-approximate method is proposed for a type of nonlinear Volterra partial integro-differential equations with a weakly singular kernel.This method is based on the fractional differential transform method (FDTM).The approximate solutions...
The Laplace-collocation method for solving fractional differential equations and a class of fractional optimal control problems
In this paper, a new numerical technique is proposed for solving fractional
differential equations where its derivative is considered in the Caputo sense.
This approach is based on a combination of the Laplace ...
An analytical and approximate solution for linear volterra partial integro-differential equation with a weakly singular kernel using the fractional differential transform method
In this paper, an analytical approximate method is proposed for solving linear Volterra partial integro-differential equations with a weakly singular kernel. This method is based on the fractional differential transform method -FDTM...
Modified fractional Euler method for solving Fuzzy Fractional Initial Value Problem
under fuzzy fractional differential equation of order ...; . Solving two
examples of linear and nonlinear FFIVP illustrates the method....
Developing a framework to establish collaborative enterprise networks
Approximation methods for solving fractional optimal control problems
In this review paper, approximation methods for the free final time of fractional optimal control problems (FOCPs) are displayed. The considered problems mainly include the fractional differential equations (FDEs) with fractional derivatives (FDs...