In this paper, we proposed a novel analytical technique for one-dimensional fractional heat equations with time derivatives subjected to the appropriate initial condition. This new technique, namely multistep reduced differential transformation method (MRDTM), is simple amendment of method, in which it treated as an algorithm sequence small intervals, order hold out accurate approximate solutions over longer frame compared traditional RDTM. The are described Caputo sense, while behavior...

Recently, many new applications in engineering and science are governed by a series of time‐fractional partial integrodifferential equations, which will lead to challenges for numerical simulation. In this article, we propose analyze an efficient iterative algorithm the solutions such equations subject initial Dirichlet boundary conditions. The provide appropriate representation infinite formula with accurately computable structures. By interrupting ‐term exact solutions, linear nonlinear...

Mathematical modeling of fractional resonant Schrödinger equations is an extremely significant topic in the classical quantum mechanics, chromodynamics, astronomy, and anomalous diffusion systems. Based on conformable residual power series, a novel effective analytical approach considered to solve classes nonlinear time-fractional equation coupled under derivatives. The solution methodology lies generating infinite series with reliable wave pattern by minimizing error functions. main...

Mathematical simulation of nonlinear physical and abstract systems is a very vital process for predicting the solution behavior fractional partial differential equations (FPDEs) corresponding to different applications in science engineering. In this paper, an attractive reliable analytical technique, conformable residual power series, implemented constructing approximate series solutions class coupled FPDEs arising fluid mechanics flow, which are often designed demonstrate weakly long waves...

In quantum field theory, the fractional Kundu-Eckhaus and massive Thirring models are nonlinear partial differential equations under sense inside Schrödinger class. this study, approximate analytical solutions of such complex acquired by means conformable residual power series method. This method presents a systematic procedure for constructing set periodic wave based on generalization gives unknown coefficients in simple pattern. By plotting behavior models; convergence regions which...

In this article, we introduce a new technique to create series solution the time-fractional Navier - Stokes equations is using combination of Laplace Transform with residual power method. Laurent presented in construction proposed method used for solving fractional physical equations. Speed and accuracy extracting an exact or approximate are most features procedure. The examined two Navier-Stokes that representing motion flow pipe. Comparisons previous methods error analysis were performed...

In this paper, reproducing kernel Hilbert space method is applied to approximate the solution of two-point boundary value problems for fourth-order Fredholm-Volterra integrodifferential equations. The analytical was calculated in form convergent series <svg style="vertical-align:-3.27605pt;width:58.737499px;" id="M1" height="19.775" version="1.1" viewBox="0 0 58.737499 19.775" width="58.737499" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g...

In this article, we introduce a novel numerical scheme, the iterative reproducing kernel method (IRKM), for providing approximate solutions of certain class time-fractional boundary value problem within favorable aspects Hilbert space in Caputo sense. The algorithm methodology is based on generating an orthonormal basis from function to formulate solution form uniformly convergent series, accordance with constraint conditions ω5[0,1]. Error estimates ω5-norm are obtained as well experiments...

This paper presents an iterative reproducing kernel algorithm for obtaining the numerical solutions of Riesz fractional diffusion and advection-dispersion equations in porous media on a finite domain. The representation exact is given W (Ω) H inner product spaces. computation required grid points relies R(y,s) (x, t) r(y,s) (x,t) functions. An efficient construction to obtain solution together with existence proof based upon theory. Numerical such acquired by interrupting n-term solution. In...

Nonclassical quantum mechanics along with dispersive interactions of free particles, long-range boson stars, hydrodynamics, harmonic oscillator, shallow-water waves, and condensates can be modeled via the nonlinear fractional Schrödinger equation. In this paper, various types optical soliton wave solutions are investigated for perturbed, conformable space-time model competed a weakly nonlocal term. The derivatives described by means sense. Two different nonlinearity discussed based on Kerr...

A powerful analytical approach, namely the fractional residual power series method (FRPS), is applied successfully in this work to solving a class of stiff systems. The methodology FRPS gets Maclaurin expansion solution rapidly convergent form and apparent sequences based on Caputo sense without any restriction hypothesis. This approach tested system with nonlinearity ranging. Meanwhile, stability convergence study are presented domain interest. Illustrative examples justify that proposed...

The mathematical structure of some natural phenomena nonlinear physical and engineering systems can be described by a combination fuzzy differential equations that often behave in way cannot fully understood. In this work, an accurate numeric-analytic algorithm is proposed, based upon the use residual power series, to investigate approximate solution for Duffing oscillator, along with suitable uncertain guesses under strongly generalized differentiability. proposed approach optimizes...