Existence and Uniqueness of Solutions for the System of Nonlinear Fractional Differential Equations with Nonlocal and Integral Boundary Conditions

Abstract

In the present study, the nonlocal and integral boundary value problems for the system of nonlinear fractional differential equations involving the Caputo fractional derivative are investigated. Theorems on existence and uniqueness of a solution are established under some sufficient conditions on nonlinear terms. A simple example of application of the main result of this paper is presented.

Some Results on Fixed and Best Proximity Points of Precyclic Self-Mappings

“…We will establish the formulation in metric spaces ( , ). It might be pointed out that it is usual to state formulations related to differential or dynamic systems and their stability, including those being formulated in a fractional calculus framework, in normed or Banach spaces since their dynamics evolve through time described by their state vectors [14,[29][30][31][32][33][34][35][36][37][38][39]. A possibility to focus on the study of their equilibrium points in a formal and structured fashion as well as their limit solutions, provided that they exist, (for instance, the presence of possible limit cycles) is through fixed point theory since the equilibrium points are fixed points of certain mappings and the limit cycles are repeated portions of limit state space trajectories.…”

Impulsive fractional differential inclusions with flux boundary conditions

“…That is why, it is owing to the fact that each of fractional calculus and impulsive theory serves very practical instruments for mathematical modeling of many concepts in different branches of science and engineering [1][2][3][4][5][6][7]. See [8][9][10][11][12][13][14][15][16][17][18][19][20][21] for some recent works on fractional differential equations and inclusions, and see [22][23][24][25][26][27][28][29][30][31] for the ones on impulsive fractional differential equations and inclusions.…”

Positive Solutions for a System of Fractional Differential Equations with Nonlocal Integral Boundary Conditions

“…Integral conditions come up when values of the function on the boundary is connected to values inside the domain or when direct measurements on the boundary are not possible, see [13,[21][22][23][24][25] Many methods are used to investigate the existence of solutions for boundary value problems, one can cite fixed point theory, the upper and lower solution method, the variational method…We refer the reader to [7][8][9][10][11][12][22][23][24][25][26][27][28][29][30][31] for recent developments in this area. On the other hand, fixed point theory is a very powerful mathematical tool in the study of boundary value problems where the existence, uniqueness, positivity and stability knowledge are needed.…”