Results 31 to 40 of about 29,735 (296)
Abstract and Applied Analysis, 2013 Two tecHniques were implemented, the Adomian decomposition method (ADM) and multivariate Padé approximation (MPA), for solving nonlinear partial differential equations of fractional order. The fractional derivatives are described in Caputo sense.
Veyis Turut, Nuran Güzel
doaj +1 more source
A Type of Fractional Power Series
, 2023 Abstract: In this paper, based on Jumarie’s modified Riemann-Liouville (R-L) fractional derivative and a new multiplication of fractional analytic functions, a type of fractional power series is studied. We can find the exact solution of this fractional power series by using some methods.
openaire +2 more sources
Toward computational algorithm for time-fractional Fokker–Planck models
Advances in Mechanical Engineering, 2019 This article describes an efficient algorithm based on residual power series to approximate the solution of a class of partial differential equations of time-fractional Fokker–Planck model. The fractional derivative is assumed in the Caputo sense.
Asad Freihet +5 more
doaj +1 more source
A Systematic Approach to Delay Functions
Mathematics, 2023 We present a systematic introduction to a class of functions that provide fundamental solutions for autonomous linear integer-order and fractional-order delay differential equations.
Christopher N. Angstmann +4 more
doaj +1 more source
Study of a Fractional Power Series
, 2023 International Journal of Recent Research in Civil and Mechanical Engineering (IJRRCME), ISSN 2393-8471, Paper Publications, Website: www.paperpublications ...
openaire +2 more sources
Some New Results on Conformable Fractional Power Series
Asia Pacific Journal of Mathematics, 2020 In this paper, some important results of the classical power series are generalized for the fractional power series. Some of these theorems are constructed by using conformable fractional derivatives. The ratio test has been specifically established to calculate the radius of convergence of a fractional power series, and several theorems of ...
Francisco Martínez +3 more
openaire +2 more sources
Results in Physics, 2019 In this paper, we present numerical analytical solutions of a fractional multi-pantograph system by using two attractive methods with rapidly convergence, control of the convergence region and easily software accounts of the infinite series solutions ...
Ahmad El-Ajou +3 more
doaj +1 more source
Discrete Dynamics in Nature and Society, 2018 This paper is devoted to studying the analytical series solutions for the differential equations with variable coefficients. By a general residual power series method, we construct the approximate analytical series solutions for differential equations ...
Bochao Chen, Li Qin, Fei Xu, Jian Zu
doaj +1 more source
Analytical solution of the time fractional Navier-Stokes equation
Ain Shams Engineering Journal, 2018 In this paper we will use the residual power series (RPS) method to generate the solution of the nonlinear time fractional Navier-Stokes equation in two dimensions in the form of a rapidly convergent series, where we adopted the definition of Caputo to ...
Khaled K. Jaber, Rami S. Ahmad
doaj +1 more source
FRACTIONAL POWER SERIES APPROACH FOR THE SOLUTION OF FRACTIONAL-ORDER INTEGRO-DIFFERENTIAL EQUATIONS
Fractals, 2021 Fractional differential and integral equations are focus of the researchers owing to their tremendous applications in different field of science and technology, such as physics, chemistry, mathematical biology, dynamical system and engineering. In this work, a power series approach called Residual Power Series Method (RPSM) is applied for the solution
Muhammad Akbar +6 more
openaire +2 more sources