Upper and Lower Solutions to a Coupled System of Nonlinear Fractional Differential Equations

Analysis of Implicit Type Nonlinear Dynamical Problem of Impulsive Fractional Differential Equations

“…The area devoted to the study of existence and uniqueness of solutions to initial/boundary value problems for fractional order differential equations has been studied very well and plenty of papers are available on it in the literature. We refer the reader to few of them in [8][9][10][11][12][13][14] and the references therein. To model evolution process and phenomena which are experienced from sudden changes in their states, impulsive differential equations serve as a powerful mathematical tool to model them.…”

Iterative scheme for a coupled system of fractional‐order differential equations with three‐point boundary conditions

“…The field of fractional-order differential equations is an important area of research and has lots of applications in almost every field of science; we refer to [1][2][3][4][5][6][7][8] for some of its applications and [9][10][11][12][13] for existence of solutions. Recently, the study of coupled systems of boundary value problems for nonlinear fractional-order differential equations has attracted some attention, and few results can be found in the literature dealing with the existence and uniqueness of solutions (see [14][15][16][17] for further reference).…”

Numerical Solutions of Coupled Systems of Fractional Order Partial Differential Equations

“…Our proposed method is simple and there is no computational complexity in the resulting algebraic system to solve. Further, we remark that our present method is a numerical method based on shifted Jacobi polynomials while the method discussed in [43] is an iterative method based on monotone iterative technique. Further we can easily establish a simple relationship for convergence of the propped method.…”