[PDF] Top 20 Series Solutions Of Fractional Initial-Value Problems By Q-Homotopy Analysis Method

... order q- HAM approximation at different values of 𝛼 and 𝑛 are drawn in figures ...the value of 𝑈 7 (𝑡; 𝛼; 𝑛) is constant at certain values of 𝑡, 𝛼 and 𝑛 ...the series solution ... See full document

... the q-homotopy analysis method ...of series solutions obtained by q-HAM is increasing as q is ...of q- HAM with the HAM and HPM was ...of q- HAM is ... See full document

... a fractional order two-point boundary value problem ...sinc-Galerkin method that has almost not been employed for the fractional order differential ...finite series in terms of composite ... See full document

... the fractional finite difference ...transform method. The authors [2] also developed and applied a transform method for fractional q-calculus ...the fractional q-calculus ... See full document

... power series method and homotopy analysis transform method, are applied for solving the initial value problem of time fractional partial differential equations with ... See full document

... approximate solutions for the stochastic process for random diffusion models with nonlinear perturbations where uncertainty is considered by means of an additive term defined by white ...HAM method is ... See full document

... the fractional Laplace decomposition method [44], the fractional ho- motopy perturbation transform method [45, 46], the fractional Adams-Bashforth method [47], and the ... See full document

... optimal homotopy asymptotic method ...as homotopy asymptotic method ...the series solution and its solution agrees with the exact one at large domains, for more infor- mation see ... See full document

... years, fractional differential equations (FDEs) have found applications in many problems in physics and engineering ...nonlinear problems include the Adomian decomposition method (ADM) [5-6], ... See full document

... novel method for finding solutions for the initial-boundary value problems (IBVPs), which is called the Sawangtong’s Green function homotopy perturbation method, shortly ... See full document

... analytical solutions of the fractional coupled mKdV equation are obtained by homotopy analysis method ...The method includes an auxiliary parameter which provides a convenient ... See full document

... fruitful method (Homotopy Analysis Method (HAM)) for solving linear and nonlinear (ordinary differential, partial differential, integral, ...this method yields a rapid convergence of ... See full document

... of solutions of nonlinear initial (or boundary) value problems of fractional equa- tions by applying nonlinear analysis such as fixed point theorems, lower and upper so- lutions ... See full document

... of fractional differential equations appears in many of the physical and engineering phenomena in the last two decades ...[1]-[3]. Problems with nonlocal conditions and related topics were studied in, for ... See full document

... of homotopy perturbation ...diversified initial boundary value problems with non local boundary ...the method, the obtained solutions are shown ...the method is easier to ... See full document

... the homotopy analysis method has been applied to solve some of engineering problems defined on an elliptical ...Exact solutions for equations of the type ∇ = 2 u b x y ( ) , and ∇ = 2 u ... See full document

... of fractional calculus and the applications of physics, mechanics and chemistry engi- neering [22, ...hybrid fractional differential equations we refer to [7], [10], [20], [24], [25] and the references ... See full document

... Presently, there is a development of boundary value problems for fractional q-difference equations showing an operation of the investigative function. The study may also have an- other ... See full document

... Note that the operator A : U → C is continuous and completely continuous. From the choice of U, there is no u ∈ ∂U such that u = λ Au for some λ ∈ (, ). Consequently, by nonlinear alternative of Leray-Schauder type ... See full document

... Mathematical modeling of enzyme kinetics is given in the books by Rubinow [10], Murray [11], Segel [12] and Roberts [13]. Recently Rajendran and his team also solved some non linear problems in enzyme reaction ... See full document