This paper is devoted to the study of a Wright-type hypergeometric function (Virchenko, Kalla and Al-Zamel in Integral Transforms Spec. Funct. 12(1):89-100, 2001) by using a Riemann-Liouville type fractional integral, a differential operator and Lebesgue measurable real or complex-valued functions. The results obtained are useful in the theory of special functions where the Wright function occurs naturally. MSC: 33C20; 33E20; 26A33; 26A99
In this paper, we have solved the non-linear Korteweg-de Vries equation by considering it in time-fraction Caputo sense and offered intrinsic properties of solitary waves. The fractional residual power series method is used to obtain the approximate solution of the aforesaid equation and compared the obtained results with Adomian Decomposition Method. Obtained results are efficient, reliable, and simple to execute on most of the non-linear fractional partial differential equations, which arise in various dynamical systems.
In present paper, we obtain functions R t(c, ν, a, b) and R t(c, −µ, a, b) by using generalized hypergeometric function. A recurrence relation, integral representation of the generalized hypergeometric function 2 R 1 (a, b; c; τ ; z) and some special cases have also been discussed.
In this article, we present a novel hybrid approach, by combining the Sawi transform with the homotopy perturbation method, to achieve the approximate and analytic solutions of nonlinear fractional differential equations (ODE as well as PDE) using the time-fractional Caputo derivative. The proposed algorithm is faster and simple compared to other iterative methods. The Sawi transform is used along with the homotopy perturbation method to accelerate the convergence of the series solution. The results discussed using calculations, graphs and tables are compatible for comparison with other known methods like the residual power series method and the exact solution which are discussed in the literature.
In the present work, the fractional‐order Sawada–Kotera–Ito problem is solved by considering nonlocal Caputo and nonsingular Atangana–Baleanu (ABC) derivatives. The methodology used is an application of the Shehu transform and the Adomian decomposition method. The obtained solution is more accurate when using the ABC type derivative as compared to the Caputo sense, when using the proposed ADShTM method (Adomian decomposition Shehu transform method). The results so obtained by the ADShTM using Caputo and ABC operators are compared, establishing the superiority of the proposed method. The numerical results demonstrate that the application of the ABC derivative is not only relatively more effective and reliable but also straightforward to achieve high precision solution.
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