In the present article, we utilize the Conformable Double Laplace transform method (CDLTM) to get the exact solutions of a wide class of Conformable fractional di, er-ential in mathematical physics. The results obtained show that the proposed method is e, cient, reliable and easy to be implemented on related linear problems in applied mathematics and physics. Moreover, the (CDLTM) has a small computational size as compared to other methods.

In the present work, we focus on solutions of K(p,p) equation which are solitons with compact support called compactons. Such a study of compact solitary waves will help us understanding solitons at a deeper level. One of the interesting feature, they govern is quasi elastic collision and gaining the same coherent shape again after scat-tering. Numerical scheme used to study the compacton solutions of K(p,p) equation is based on reduced di, erential transform method. Both one dimensional di, eren-tial transform method and two dimensional reduced di, erential transform method have been used. Test problems under consideration show the e, cient working of the proposed scheme.

By adding a suitable real function on both sides of the quadratic Riccati differential equation, we propose a weighted type of Adams-Bashforth rules for solving it, in which moments are used instead of the constant coefficients of Adams-Bashforth rules. Numerical results reveal that the proposed method is efficient and can be applied for other nonlinear problems.

In the present work, we focus on solutions of K(p,p) equation which are solitons with compact support called compactons. Such a study of compact solitary waves will help us understanding solitons at a deeper level. One of the interesting feature, they govern is quasi elastic collision and gaining the same coherent shape again after scat-tering. Numerical scheme used to study the compacton solutions of K(p,p) equation is based on reduced di, erential transform method. Both one dimensional di, eren-tial transform method and two dimensional reduced di, erential transform method have been used. Test problems under consideration show the e, cient working of the proposed scheme.

In this paper, we propose a new numerical algorithm for the approximate solution of non-homogeneous fractional di, erential equation. Using this algorithm the fractional di, erential equations are transformed into a system of algebraic linear equations by operational matrices of block-pulse and hybrid functions. Based on our new algorithm, this system of algebraic linear equations can be solved by a proposed (TSI) method. Further, some numerical examples are given to illustrate and establish the accuracy and reliability of the proposed algorithm.

This paper is devoted to obtaining an analytical solution for the second-order fuzzy di, erential equations by considering the type of generalized Hukuhara di, erentiability of the solution. The e, ective-ness and e, ciency of the approaches are illustrated by solving several practical examples such as the fuzzy Cauchy-Euler equation, the fuzzy Legendre equation, and the fuzzy Chebyshev di, erential equation.

In this paper, we present a numerical method for solving fuzzy di erential equation of fractional order under gH-fractional Caputo di erentiability. The main idea of this method is to approximate the solution of fuzzy fractional di erential equation (FFDE) by an implicit method as corrector and explicit method as predictor. This method is tested on numerical examples.

In this paper, the sinc collocation method is proposed for solving linearand nonlinear multi-order fractional di erential equations based on the newde nition of fractional derivative which is recently presented by Khalil, R., Al Horani, M., Yousef, A. and Sababeh, M. in A new de nition of fractionalderivative, J. Comput. Appl. Math. 264 (2014), 65{70. The propertiesof sinc functions are used to reduce the fractional di erential equation to asystem of algebraic equations. Several numerical examples are provided toillustrate the accuracy and e ectiveness of the presented method.