Computation of solution to fractional order partial reaction diffusion equations

Abstract

Graphical abstract

Three new approaches for solving a class of strongly nonlinear two-point boundary value problems

“…For solving this equation, we apply generalized Coiflet scaling functions. Using equation ( 8), we approximate the unknown function as ν(x) = ν j (x) and substitute it in equation (27). Now we utilize the collocation method with mesh points τ i = i 2 j , i = 0, 1, .…”

“…Wavelets were applied in numerically solving the integro-differential and differential equations [14,15]. Also the hybrid methods, combination of some analytical and numerical methods, were successfully employed to achieve the solutions of initial and boundary value problems; for instance, see [16,17,26,27]. In this paper we apply three different methods based on a quasi-linearization technique, the homotopy analysis method based Coiflet orthogonal scaling functions, and an efficient approach for transforming the aforementioned equation to an integral equation.…”

Application of Asymptotic Homotopy Perturbation Method to Fractional Order Partial Differential Equation

“…In this regard, various types of techniques have been developed for numerical solutions of non-linear and linear differential equations of integer order. However, there are very few schemes that have been extended to find the solution of linear and nonlinear differential equations of fractional order; for reading, see [12][13][14][15][16][17]. In this article, we desire to contribute to and extend the recent technique asymptotic homotopy perturbation method (AHPM) for the solution of real-world problems.…”

Conserved quantities, optimal system and explicit solutions of a (1 + 1)-dimensional generalised coupled mKdV-type system

“…Nonlinear partial differential equations (NLPDEs) have rapidly become indispensable in the quest to conceptualise the world around us [1] , [2] , [3] , [4] , [5] , [6] , [7] , [8] , [9] , [10] , [11] , [12] , [13] , [14] , [15] , [16] , [17] , [18] , [19] , [20] , [21] , [22] , [23] , [24] , [25] , [26] , [27] , [28] , [29] , [30] , [31] , [32] , [33] , [34] , [35] , [36] , [37] , [38] , [39] , [40] , [41] , [42] , [43] , [44] , [45] , [46] , [47] , [48] , [49] , [50] . We give a few recent studies of NLPDEs presented in the literature.…”

“…For instance, the numerical treatments to a complex order fractional nonlinear one-dimensional problem of Burgers equations was discussed in [1] . Computation of solutions to fractional order partial reaction diffusion equations was presented in [2] . Kadomtsev–Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equation was investigated in [3] and exact solutions were constructed.…”