A Numerical Algorithm for the Solutions of ABC Singular Lane–Emden Type Models Arising in Astrophysics Using Reproducing Kernel Discretization Method

Numerical Algorithm for the Solutions of Fractional Order Systems of Dirichlet Function Types with Comparative Analysis

(2019) Omar Abu Arqub   FUNDAMENTA INFORMATICAE

Generalized exponential rational function method for extended Zakharov–Kuzetsov equation with conformable derivative

(2019) Behzad Ghanbari et al.   MODERN PHYSICS LETTERS A

New analytical study of water waves described by coupled fractional variant Boussinesq equation in fluid dynamics

(2019) M S Osman   PRAMANA-JOURNAL OF PHYSICS

A general bilinear form to generate different wave structures of solitons for a (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation

(2019) M. S. Osman et al.   MATHEMATICAL METHODS IN THE APPLIED SCIENCES

Different complex wave structures described by the Hirota equation with variable coefficients in inhomogeneous optical fibers

(2019) Jian-Guo Liu et al.   APPLIED PHYSICS B-LASERS AND OPTICS

Fitted fractional reproducing kernel algorithm for the numerical solutions of ABC – Fractional Volterra integro-differential equations

(2019) Omar Abu Arqub et al.   CHAOS SOLITONS & FRACTALS

Modulation of reproducing kernel Hilbert space method for numerical solutions of Riccati and Bernoulli equations in the Atangana-Baleanu fractional sense

(2019) Omar Abu Arqub et al.   CHAOS SOLITONS & FRACTALS

Complex wave structures for abundant solutions related to the complex Ginzburg–Landau model

(2019) M.S. Osman et al.   OPTIK

New analytical wave structures for the (3 + 1)-dimensional Kadomtsev-Petviashvili and the generalized Boussinesq models and their applications

(2019) D. Lu et al.   Results in Physics

An adaptive numerical approach for the solutions of fractional advection–diffusion and dispersion equations in singular case under Riesz’s derivative operator

(2019) Omar Abu Arqub et al.   PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS

Numerical solutions for the Robin time-fractional partial differential equations of heat and fluid flows based on the reproducing kernel algorithm

(2018) Omar Abu Arqub   INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW

Numerical solutions of time-fractional partial integrodifferential equations of Robin functions types in Hilbert space with error bounds and error estimates

(2018) Omar Abu Arqub et al.   NONLINEAR DYNAMICS

Decolonisation of fractional calculus rules: Breaking commutativity and associativity to capture more natural phenomena

(2018) Abdon Atangana et al.   European Physical Journal Plus

Numerical solutions of systems of first-order, two-point BVPs based on the reproducing kernel algorithm

(2018) Omar Abu Arqub   CALCOLO

Fractional derivatives with no-index law property: Application to chaos and statistics

(2018) Abdon Atangana et al.   CHAOS SOLITONS & FRACTALS

Numerical solutions of integrodifferential equations of Fredholm operator type in the sense of the Atangana–Baleanu fractional operator

(2018) Omar Abu Arqub et al.   CHAOS SOLITONS & FRACTALS

Atangana–Baleanu fractional approach to the solutions of Bagley–Torvik and Painlevé equations in Hilbert space

(2018) Omar Abu Arqub et al.   CHAOS SOLITONS & FRACTALS

Abundant complex wave solutions for the nonautonomous Fokas–Lenells equation in presence of perturbation terms

(2018) Yao Ding et al.   OPTIK

Computational algorithm for solving fredholm time-fractional partial integrodifferential equations of dirichlet functions type with error estimates

(2018) Mohammed Al-Smadi et al.   APPLIED MATHEMATICS AND COMPUTATION

Solutions of time-fractional Tricomi and Keldysh equations of Dirichlet functions types in Hilbert space

(2017) Omar Abu Arqub   NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

Numerical algorithm for solving time-fractional partial integrodifferential equations subject to initial and Dirichlet boundary conditions

(2017) Omar Abu Arqub et al.   NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

On the new fractional derivative and application to nonlinear Fisher’s reaction–diffusion equation

(2016) Abdon Atangana   APPLIED MATHEMATICS AND COMPUTATION

Comparing the Atangana–Baleanu and Caputo–Fabrizio derivative with fractional order: Allen Cahn model

(2016) Obaid Jefain Julaighim Algahtani   CHAOS SOLITONS & FRACTALS

New exact solutions of nonlinear fractional acoustic wave equations in ultrasound

(2016) S. Saha Ray   COMPUTERS & MATHEMATICS WITH APPLICATIONS

Approximate Solutions of DASs with Nonclassical Boundary Conditions using Novel Reproducing Kernel Algorithm

(2016) Omar Abu Arqub   FUNDAMENTA INFORMATICAE

The reproducing kernel algorithm for handling differential algebraic systems of ordinary differential equations

(2016) Omar Abu Arqub   MATHEMATICAL METHODS IN THE APPLIED SCIENCES

Application of reproducing kernel algorithm for solving second-order, two-point fuzzy boundary value problems

(2016) Omar Abu Arqub et al.   SOFT COMPUTING

New fractional derivatives with nonlocal and non-singular kernel: Theory and application to heat transfer model

(2016) Abdon Atangana et al.   Thermal Science

A novel expansion iterative method for solving linear partial differential equations of fractional order

(2015) Ahmad El-Ajou et al.   APPLIED MATHEMATICS AND COMPUTATION

Constructing and predicting solitary pattern solutions for nonlinear time-fractional dispersive partial differential equations

(2015) Omar Abu Arqub et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Approximate analytical solution of the nonlinear fractional KdV–Burgers equation: A new iterative algorithm

(2015) Ahmad El-Ajou et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Analytical approximate solutions of Riesz fractional diffusion equation and Riesz fractional advection-dispersion equation involving nonlocal space fractional derivatives

(2015) S. Saha Ray et al.   MATHEMATICAL METHODS IN THE APPLIED SCIENCES

Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm–Volterra integrodifferential equations

(2015) Omar Abu Arqub   NEURAL COMPUTING & APPLICATIONS

Numerical solutions of fuzzy differential equations using reproducing kernel Hilbert space method

(2015) Omar Abu Arqub et al.   SOFT COMPUTING

Numerical solutions of fractional differential equations of Lane-Emden type by an accurate technique

(2015) Ali Akgül et al.   Advances in Difference Equations

Numerical solution for the model of RLC circuit via the fractional derivative without singular kernel

(2015) Abdon Atangana et al.   Advances in Mechanical Engineering

Numerical algorithm for solving two-point, second-order periodic boundary value problems for mixed integro-differential equations

(2014) Omar Abu Arqub et al.   APPLIED MATHEMATICS AND COMPUTATION

Solving Fredholm integro–differential equations using reproducing kernel Hilbert space method

(2013) Omar Abu Arqub et al.   APPLIED MATHEMATICS AND COMPUTATION

A numerical method for singularly perturbed turning point problems with an interior layer

(2013) F.Z. Geng et al.   JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

A collocation method based on reproducing kernel for a modified anomalous subdiffusion equation

(2013) Wei Jiang et al.   NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

Application of optimal homotopy asymptotic method for the analytic solution of singular Lane–Emden type equation

(2011) S. Iqbal et al.   APPLIED MATHEMATICS AND COMPUTATION

Solution of Lane–Emden type equations using Bernstein operational matrix of differentiation

(2011) Rajesh K. Pandey et al.   NEW ASTRONOMY

An analytic algorithm of Lane–Emden type equations arising in astrophysics using modified Homotopy analysis method

(2009) Om P. Singh et al.   COMPUTER PHYSICS COMMUNICATIONS

Numerical Methods for the Variable-Order Fractional Advection-Diffusion Equation with a Nonlinear Source Term

(2009) P. Zhuang et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS