Related papers: ARA-residual power series method for solving parti…
This paper investigates analytical approximate solutions for a system of multipantograph delay differential equations using the residual power series method (RPSM), which obtains a Taylor expansion of the solutions and produces the exact…
Fractional nonlinear differential equations present an interplay between two common and important effective descriptions used to simplify high dimensional or more complicated theories: nonlinearity and fractional derivatives. These…
Power Series Solution method has been used traditionally for to solve Linear Differential Equations, in Ordinary and Partial form. But this method has been limited to this kind of problems. We present the solution of problems of Non Linear…
This paper is concerned with an alternative analytical solution of time-fractional nonlinear Schrodinger equation and nonlinear coupled Schrodinger equation obtained by employing fractional reduced differential transform method. The…
This analysis proposes an analytical-numerical approach for providing solutions of a class of nonlinear fractional Klein-Gordon equation subjected to appropriate initial conditions in Caputo sense by using the Fractional Reduced…
We consider a time fractional differential equation of order $\alpha$, $0<\alpha<1$, $$ \frac{\partial c(x,t)}{\partial t}={}^C_0\mathcal{D}_t^{\alpha}[(Ac)(x,t)]+q(x,t) ,\quad x > 0, t > 0, \quad c(x,0)=f(x). $$ where…
In this paper, a nonlinear system of fractional ordinary differential equations with multiple scales in time is investigated. We are interested in the effective long-term computation of the solution. The main challenge is how to obtain the…
Recently, a new fractional derivative called the conformable fractional derivative is given which is based on the basic limit definition of the derivative in [1]. Then, the fractional versions of chain rules, exponential functions,…
In this paper, we present analytic-approximate solution of a fractional Zakharov-Kuznetsov equation by means of perturbation-iteration algorithm (PIA) and residual power series method (RSPM). Basic definitions of fractional derivatives are…
Power Series Solution Method has been traditionally used to solve Ordinary and Partial Linear Differential Equations. However, despite their usefulness the application of this method has been limited to this particular kind of equations. In…
The following document presents some novel numerical methods valid for one and several variables, which using the fractional derivative, allow to find solutions for some non-linear systems in the complex space using real initial conditions.…
The aim of this paper is to solve numerically, using the meshless method via radial basis functions, time-space-fractional partial differential equations of type Black-Scholes. The time-fractional partial differential equation appears in…
This paper introduces the Asad Correctional Power Series Method (ACPS), a novel and groundbreaking approach designed to simplify and optimize the solution of fractional differential equations. The ACPS combines algebraic manipulation with…
We develop a high accuracy power series method for solving partial differential equations with emphasis on the nonlinear Schr\"odinger equations. The accuracy and computing speed can be systematically and arbitrarily increased to orders of…
The time-fractional Fokker-Planck equation is a key model for characterizing anomalous diffusion, stochastic transport, and non-equilibrium statistical mechanics with applications in finance, chaotic dynamics, optical physics, and…
The Residual Power Series Method (RPSM) provides a powerful framework for solving fractional differential equations. However, a significant computational bottleneck arises from the necessity of calculating the fractional derivatives of the…
The accuracy of the numerical solution of a fractional differential equation depends on the differentiability class of the solution. The derivatives of the solutions of fractional differential equations often have a singularity at the…
In this paper, we propose an RADI-type method for large-scale stochastic continuous-time algebraic Riccati equations with sparse and low-rank matrices. This new variant of RADI-type methods is developed by integrating the core concept of…
In this study, we focus on identifying solution and an unknown space-dependent coefficient in a space-time fractional differential equation by employing fractional Taylor series method. The substantial advantage of this method is that we…
In this work we present a power series method for solving ordinary and partial differential equations. To demonstrate our method we solve a system of ordinary differential equations describing the movement of a random walker on a…