On Coupledp-Laplacian Fractional Differential Equations with Nonlinear Boundary Conditions

Abstract

This paper is related to the existence and uniqueness of solutions to a coupled system of fractional differential equations (FDEs) with nonlinear -Laplacian operator by using fractional integral boundary conditions with nonlinear term and also to checking the Hyers-Ulam stability for the proposed problem. The functions involved in the proposed coupled system are continuous and satisfy certain growth conditions. By using topological degree theory some conditions are established which ensure the existence and uniqueness of solution to the proposed problem. Further, certain conditions are developed corresponding to Hyers-Ulam type stability for the positive solution of the considered coupled system of FDEs. Also, from applications point of view, we give an example.

Positive solutions for a system of nonlinear fractional nonlocal boundary value problems with parameters and p-Laplacian operator

“…The system of fractional differential equations boundary value problems with pLaplacian operator have also received much attention and have developed very rapidly, see [24][25][26][27][28][29][30][31][32]. In [24], Li et al studied the following fractional differential system involving the p-Laplacian operator and nonlocal boundary conditions:…”

“…The uniqueness of solution was established by using the Banach contraction mapping principle. Khan et al [31] considered the existence and uniqueness of solutions to a coupled system of fractional differential equations with p-Laplacian operator. The functions involved in the proposed coupled system were continuous and satisfied certain growth conditions.…”

Existence of solution for a fractional‐order Lotka‐Volterra reaction‐diffusion model with Mittag‐Leffler kernel

“…In order to continue study about the L‐V model of fractional order in ABC sense of derivative , we suggest the readers for reconsideration of for the study of exact traveling wave front, multiplicity, and exponential stability. Some more related results on dynamical models may be studied in …”

Stability analysis and a numerical scheme for fractional Klein‐Gordon equations

“…One can see in the references of the paper some useful applications of FDEs in viscoelasticity, bioengineering, damping laws, rheology, thermodynamics, synchronization, dynamical system, electrical circuits, signal processing, and fluid mechanics, see. [1][2][3][4][5][6][7][8][9][10][11][12][13] The fractional order Klein-Gordon equation (KGE) is derived from the KGE of the integer order by switching time derivative by noninteger order ( ∈ [0, 1]) derivative. The fractional order KGE can be illustrated as below:…”