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A fractional time derivative is introduced into the Burger's equation to model losses of nonlinear waves. This term amounts to a time convolution product, which greatly penalizes the numerical modeling. A diffusive representation of the…

Computational Physics · Physics 2016-06-14 Bruno Lombard , Denis Matignon

A generalization of the Hopf-Cole transformation and its relation to the Burgers equation of integer order and the diffusion equation with quadratic nonlinearity are discussed. The explicit form of a particular analytical solution is…

Analysis of PDEs · Mathematics 2013-02-26 Paulius Miskinis

In this note, we consider some Burgers-like equations involving Laguerre derivatives and demonstrate that it is possible to construct specific exact solutions using separation of variables. We prove that a general scheme exists for…

General Mathematics · Mathematics 2024-09-06 Giuseppe Dattoli , Riccardo Droghei , Roberto Garra

In many mathematical types of research, in order to solve the fuzzy fractional differential equations, we should transform these problems into crisp corresponding problems and by solving them the approximate solution can be obtained. The…

General Mathematics · Mathematics 2020-11-02 T. Allahviranloo , Z. Noeiaghdam , S. Noeiaghdam , S. Salahshour , Juan J. Nieto

In this paper we investigate the solution of generalized distributed order diffusion equations with composite time fractional derivative by using the Fourier-Laplace transform method. We represent solutions in terms of infinite series in…

Mathematical Physics · Physics 2017-03-17 Trifce Sandev , Zivorad Tomovski , Bojan Crnkovic

We adopt a procedure of operational-umbral type to solve the $(1+1)$-dimensional fractional Fokker-Planck equation in which time fractional derivative of order $\alpha$ ($0 < \alpha < 1$) is in the Riemann-Liouville sense. The technique we…

Mathematical Physics · Physics 2018-02-27 K. Górska , A. Lattanzi , G. Dattoli

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,…

Classical Analysis and ODEs · Mathematics 2016-02-19 Emrahünal , Ahmet Gökdoğan

This paper deals with the investigation of the computational solutions of an unified fractional reaction-diffusion equation, which is obtained from the standard diffusion equation by replacing the time derivative of first order by the…

Analysis of PDEs · Mathematics 2012-10-05 R. K. Saxena , A. M. Mathai , H. J. Haubold

wave solutions to nonlinear partial differential equations. We simplify the so called (G'/G)-expansion method and apply two of those methods to simple physical problems.

Mathematical Physics · Physics 2009-02-24 Francisco M. Fernandez

This work is concerned with the study of explicit solutions for generalized coupled reaction-diffusion and Burgers-type systems with variable coefficients. Including nonlinear models with variable coefficients such as diffusive…

Mathematical Physics · Physics 2024-06-26 José M. Escorcia , Erwin Suazo

A Lax pair consisting of the Forsyth-Hopf-Cole transformation and a linear differential (in time) - difference (in continuous space) equation generates the whole hierarchy of the Burgers equation and admits exact moving front solutions.…

Exactly Solvable and Integrable Systems · Physics 2007-05-23 Alex Veksler , Yair Zarmi

The conformable time fractional Jimbo-Miwa and Zakharov-Kuznetsov equations are solved by the generalized form of the Kudryashov method. A simple compatible wave transformation is employed to reduce the dimension of the equations to one.…

Exactly Solvable and Integrable Systems · Physics 2017-06-02 Alper Korkmaz , Ozlem Ersoy Hepson

In this work, we use the spectral Galerkin method to prove the existence of a pathwise unique mild solution of a fractional stochastic partial differential equation of Burgers type in a H\"older space. We get the temporal regularity and…

Analysis of PDEs · Mathematics 2017-12-29 Zineb Arab , Latifa Debbi

In this work we derive new analytic expressions for fixation time in Wright-Fisher model with selection. The three standard cases for fixation are considered: fixation to zero, to one or both. Second order differential equations for…

Populations and Evolution · Quantitative Biology 2022-05-16 Vincent Runge , Arnaud Liehrmann , Pauline Spinga

The object of this paper is to present a computable solution of a fractional partial differential equation associated with a Riemann-Liouville derivative of fractional order as the time-derivative and Riesz-Feller fractional derivative as…

Mathematical Physics · Physics 2011-10-03 R. K. Saxena , A. M. Mathai , H. J. Haubold

Explicit solutions of differential equations of complex fractional orders with respect to functions and with continuous variable coefficients are established. The representations of solutions are given in terms of some convergent infinite…

Classical Analysis and ODEs · Mathematics 2021-03-15 Joel E. Restrepo , Michael Ruzhansky , Durvudkhan Suragan

The Riemann-Liouville fractional integrals and derivatives are generalized for cases when fractional exponent $d$ are functions of space and times coordinates (i.e. $d=d({\bf r}(t),t)$).

Classical Analysis and ODEs · Mathematics 2007-05-23 L. Ya. Kobelev

Fractional calculus of variation plays an important role to formulate the non-conservative physical problems. In this paper we use semi-inverse method and fractional variational principle to formulate the fractional order generalized…

Analysis of PDEs · Mathematics 2017-12-21 Uttam Ghosh , Susmita Sarkar , Shantanu Das

Let $f,g:{\Bbb R}\to{\Bbb R}$ be integrable functions, $f$ nowhere zero, and $\phi (u)=\int du/f(u)$ be invertible. An exact solution to the generalized nonhomogeneous inviscid Burgers' equation $u_t+g(u).u_x=f(u)$ is given, by quadratures.

Differential Geometry · Mathematics 2009-08-26 Mehdi Nadjafikhah

This article presents a finite element scheme with Newton's method for solving the time-fractional nonlinear diffusion equation. For time discretization, we use the fractional Crank-Nicolson scheme based on backward Euler convolution…

Analysis of PDEs · Mathematics 2018-11-26 Dileep Kumar , Sudhakar Chaudhary , V. V. K Srinivas Kumar