Monotone iterative technique for solving finite difference systems of time fractional parabolic equations with initial/periodic conditions

On the complex properties of the first equation of the Kadomtsev-Petviashvili hierarchy

“…Parametric conditions for validity of solutions have also been reported. Finally, we have plotted the surfaces of various solutions in 2D, 3D and contour sides by Figures (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16) with the help of some powerful computation programs. The proposed schemes supply many new coefficients which produce new properties of the model when we compare these results with existing papers.…”

“…Many analytical and numerical methods used to obtain the solutions of these models have been applied by experts from all over the world. More recently, many important powerful methods have been presented to literature namely the analytical and numerical methods [1][2][3][4], the Darboux transformations [5], the TFM [6,7], the sine-Gordon expansion method [8][9][10], the ( G G , 1 G )-expansion method [11], the (m+1/G) expansion method [12], the Lie group analysis [13], the Jacobi elliptic function method [14,15], the generalized new auxiliary equation method [16], the modified ( w g )-expansion method [17], the generalized Kudryashov method [18], the auxiliary equation method [19], the generalized exponential rational function method [20], the newly extended direct algebraic technique [21], the generalized bilinear form [22], the Hirota bilinear form [23][24][25], the transformed rational function method [26], the polynomial expansion method [27], the modified simple equation approach [28], the auto-Bäcklund transformation [29], the generalized bilinear operator [30], the extended homoclinic test approach [31], the bilinear forms [32,33], the extended tanh-function method [34] and so on [35][36][37][38][39]…”

On Solutions to Fractional Iterative Differential Equations with Caputo Derivative

“…Nowadays, the existence of solution and computing solutions by iterative schemes for equations involving fractional derivatives are research area. We may lead the reader to the recent papers [24,25], respectively. Te existence and uniqueness of fractional iterative diferential equations have been studied widely by the fxed-point theorem [9,26,27].…”