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Fractional boundary value problems
We study some functionals associated with a process driven by a fractional boundary value problem (FBVP for short). By FBVP we mean a Cauchy problem...
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A Difference Scheme with Intrinsic Parallelism for Fractional Diffusion-wave Equation with Dam**
Anomalous diffusion is a widespread physical phenomenon, and numerical methods of fractional diffusion models are of important scientific...
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Existence and uniqueness of a weak solution to fractional single-phase-lag heat equation
In this article, we study the existence and uniqueness of a weak solution to the fractional single-phase lag heat equation. This model contains the...
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A novel computational approach to the local fractional Lonngren wave equation in fractal media
The main purpose of this paper is to investigate the local fractional Lonngren wave equation, which is a generalization of Lonngren wave equation in...
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Atoms and Photons: Kinetic Equations with Delay
In his recent works, the author drew attention to the fact that the extraction of a part of a closed Hamiltonian system turns the original well-known...
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Shifted Jacobi polynomials for nonlinear singular variable-order time fractional Emden–Fowler equation generated by derivative with non-singular kernel
In this work, a nonlinear singular variable-order fractional Emden–Fowler equation involved with derivative with non-singular kernel (in the...
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Numerical Solution of the Burgers’ Equation Using Chelyshkov Polynomials
A numerical approach to approximate the nonlinear Burgers’ equation solution is presented in this article. By temporally discretizing the problem...
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A Spatially Sixth-Order Hybrid L1-CCD Method for Solving Time Fractional Schrödinger Equations
We consider highly accurate schemes for nonlinear time fractional Schrödinger equations (NTFSEs). While an L1 strategy is employed for approximating...
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On skewed grid point iterative method for solving 2D hyperbolic telegraph fractional differential equation
This paper presents the development of a new iterative method for solving the two-dimensional hyperbolic telegraph fractional differential equation...
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A novel iterative solution for time-fractional Boussinesq equation by reproducing kernel method
In this study, iterative reproducing kernel method (RKM) will be applied in order to observe the effect of the method on numerical solutions of...
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Transparent boundary conditions and numerical computation for singularly perturbed telegraph equation on unbounded domain
In this paper, we study the numerical solution for the singularly perturbed telegraph equation (SPTE) on unbounded domain. Firstly, we investigate...
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Some Results on Generalized Accelerated Motions Driven by the Telegraph Process
We investigate a generalization of the randomly accelerated motion obtained by iterated integration of the telegraph signal. We give the exact and...
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Boubaker operational matrix method for solving fractional weakly singular two-dimensional partial Volterra integral equation
The aim of the present paper is to suggest a novel technique based on the operational matrix approach for solving a fractional weakly singular...
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Numerical Study of Conformable Space and Time Fractional Fokker–Planck Equation via CFDT Method
In this article, conformable fractional differential transform (CFDT) method has been successfully implemented to compute the numerical solution of...
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Numerical Methods for Solving a Riesz Space Partial Fractional Differential Equation: Applied to Fractional Kinetic Equations
In this paper, we design new numerical methods for solving the partial fractional differential equations. The fractional kinetics equation has been...
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Numerical solution of time-fractional Kawahara equation using reproducing kernel method with error estimate
We present a new approach depending on reproducing kernel method (RKM) for time-fractional Kawahara equation with variable coefficient. This approach...
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Parameter Identification of Fractional Order Partial Differential Equation Model Based on Polynomial–Fourier Method
Parameter identification plays a crucial role in the study of dynamics for fractional order structural models. This article introduces an innovative...
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A radial basis function-Hermite finite difference (RBF-HFD) method for the cubic-quintic complex Ginzburg–Landau equation
In this paper, the cubic–quintic complex Ginzburg–Landau (CQCGL) equation is numerically studied in 1D, 2D and 3D spaces. First, by the Strang...
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Generalized least square homotopy perturbation solution of fractional telegraph equations
In this paper, we present generalized aspect of least square homotopy perturbation method (generalized LSHPM) using fractional calculus. We consider...
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Spectral Solutions with Error Analysis of Volterra–Fredholm Integral Equation via Generalized Lucas Collocation Method
In this article, the solution for Volterra–Fredholm integral equation (V–FIE) is investigated numerically by using the generalized Lucas polynomials....
