The time fractional order differential equations are fundamental tools that are used for modeling neuronal dynamics. These equations are obtained by substituting the time derivative of order where , in the standard equation with the Caputo fractional formula. In this paper, two implicit difference schemes: the linearly Euler implicit and the Crank-Nicolson (CN) finite difference schemes, are employed in solving a one-dimensional time-fractional semilinear equation with Dirichlet boundary conditions. Moreover, the consistency, stability and convergence of the proposed schemes are investigated. We prove that the IEM is unconditionally stable, while CNM is conditionally stable. Furthermore, a comparative study between these two schemes will be conducted via numerical experiments. The efficiency of the proposed schemes in terms of absolute errors, order of accuracy and computing time will be reported and discussed.
Autism Spectrum Disorder, also known as ASD, is a neurodevelopmental disease that impairs speech, social interaction, and behavior. Machine learning is a field of artificial intelligence that focuses on creating algorithms that can learn patterns and make ASD classification based on input data. The results of using machine learning algorithms to categorize ASD have been inconsistent. More research is needed to improve the accuracy of the classification of ASD. To address this, deep learning such as 1D CNN has been proposed as an alternative for the classification of ASD detection. The proposed techniques are evaluated on publicly available three different ASD datasets (children, Adults, and adolescents). Results strongly suggest that 1D
... Show MoreThis paper concentrates on employing the -difference equations approach to prove another generating function, extended generating function, Rogers formula and Mehler’s formula for the polynomials , as well as thegenerating functions of Srivastava-Agarwal type. Furthermore, we establish links between the homogeneous -difference equations and transformation formulas.
An Alternating Directions Implicit method is presented to solve the homogeneous heat diffusion equation when the governing equation is a bi-harmonic equation (X) based on Alternative Direction Implicit (ADI). Numerical results are compared with other results obtained by other numerical (explicit and implicit) methods. We apply these methods it two examples (X): the first one, we apply explicit when the temperature .
The idea of the paper is to consolidate Mahgoub transform and variational iteration method (MTVIM) to solve fractional delay differential equations (FDDEs). The fractional derivative was in Caputo sense. The convergences of approximate solutions to exact solution were quick. The MTVIM is characterized by ease of application in various problems and is capable of simplifying the size of computational operations. Several non-linear (FDDEs) were analytically solved as illustrative examples and the results were compared numerically. The results for accentuating the efficiency, performance, and activity of suggested method were shown by comparisons with Adomian Decomposition Method (ADM), Laplace Adomian Decompos
... Show MoreThe power factors and electronic thermal conductivities in bismuth telluride (Bi2Te3), lead-telluride (PbTe), and gallium arsenide (GaAs) at room temperature (300K) quantum wires and quantum wells are theoretically investigated. Our formalism rigorously takes into account modification of these power factors and electronic thermal conductivities in free-surface wires and wells due to spatial confinement. From our numerical results, we predict a significant increase of the power factor in quantum wires with diameter w=20 Ã…. The increase is always stronger in quantum wires than in quantum wells of the corresponding dimensions. An unconfined phonon distribution assumed based on the bulk lattice thermal conductivity is then employed
... Show MoreIn this paper we shall prepare an sacrificial solution for fuzzy differential algebraic equations of fractional order (FFDAEs) based on the Adomian decomposition method (ADM) which is proposed to solve (FFDAEs) . The blurriness will appear in the boundary conditions, to be fuzzy numbers. The solution of the proposed pattern of equations is studied in the form of a convergent series with readily computable components. Several examples are resolved as clarifications, the numerical outcomes are obvious that the followed approach is simple to perform and precise when utilized to (FFDAEs).
In this paper we shall prepare an sacrificial solution for fuzzy differential algebraic equations of fractional order (FFDAEs) based on the Adomian decomposition method (ADM) which is proposed to solve (FFDAEs) . The blurriness will appear in the boundary conditions, to be fuzzy numbers. The solution of the proposed pattern of equations is studied in the form of a convergent series with readily computable components. Several examples are resolved as clarifications, the numerical outcomes are obvious that the followed approach is simple to perform and precise when utilized to (FFDAEs).