Fractional Solutions of Bessel Equation with -Method

Abstract

This paper deals with the design fractional solution of Bessel equation. We obtain explicit solutions of the equation with the help of fractional calculus techniques. Using the N-fractional calculus operator N ν method, we derive the fractional solutions of the equation.

Two novel computational techniques for fractional Gardner and Cahn‐Hilliard equations

“…[27][28][29][30][31][32][33] Since most of the complex phenomena are modeled mathematically by nonlinear fractional differential equations, there are many methods in the literature to solve these equations. [27][28][29][30][31][32][33] Since most of the complex phenomena are modeled mathematically by nonlinear fractional differential equations, there are many methods in the literature to solve these equations.…”

“…The analytical and numerical solutions for the nonlinear fractional differential equations have fundamental importance. [27][28][29][30][31][32][33] Since most of the complex phenomena are modeled mathematically by nonlinear fractional differential equations, there are many methods in the literature to solve these equations. The Gardner and Cahn-Hilliard equations are studied through distinct techniques such as reduced differential transform method, 34 the modified Kudryashov technique, 35 Adomian decomposition method (ADM), 36 improved (G ′ /G) − expansion method, 37 homotopy perturbation method (HPM), 26 residual power series method (RPSM), 22 and many others.…”

An Application of the Sonine–Letnikov Fractional Derivative for the Radial Schrödinger Equation

“…It is possible to see many works based on the Sonine-Letnikov fractional derivative, although it is often known as N-fractional calculus operator. These works include the solutions of the Gauss equation [12], solutions of modified Whittaker equations [13], an almost free damping vibration equation [14], differential operators and integral operators in univalent function theory [15], geometric univalent function theory [16], power and logarithmic functions, Weber's equation, Gauss hypergeometric equations and some double infinite, finite and mixed sums [17], products of some power functions and some doubly infinite sums [18], some composite functions [19], some algebraic functions [20], some functions which include a root sign [21], a modified hydrogen atom equation [22], some second order homogeneous Euler's equation [23], some logarithmic functions and some identities [24], fractional solutions of homogeneous and nonhomogeneous Chebyshev's equations [25,26], explicit solutions of Gegenbauer equation [27], fractional solutions of Bessel equation [28], fractional solutions of the radial part in the fractional Schrödinger equation [29] and some singular differential equations [30].…”

Classifications on the travelling wave solutions to the (3+1)-dimensional generalized KP and Jimbo-Miwa equations

“…Various methods have been implemented to obtain different types of solutions to the equations mentioned above such as Backlund transformation [13], the simplified Hirota's method [14], the simplified Hirota's direct method [15], the exp-function method [4], the generalized tanh method [16], the Xu's stable-range method and logarithmic generalization of stable-range method [17], the Kudryashov method [18], the homogeneous balance method [19] and many more methods. Moreover fractional concepts are investigated in [20,21,22]. …”