Existence and uniqueness of solutions for a fractional boundary value problem on a graph

Abstract

In this paper, the authors consider a nonlinear fractional boundary value problem defined on a star graph. By using a transformation, an equivalent system of fractional boundary value problems with mixed boundary conditions is obtained. Then the existence and uniqueness of solutions are investigated by fixed point theory.MSC 2010 : Primary 34B15; Secondary 34B45

Existence and Stability Results for a Fractional Order Differential Equation with Non-Conjugate Riemann-Stieltjes Integro-Multipoint Boundary Conditions

“…The nonlocal boundary conditions are found to be of great utility in modeling the changes happening within the domain of the given scientific phenomena, while the concept of integral boundary conditions is applied to model the physical problems, such as blood flow problems on arbitrary structures and ill-posed backward problems. For some recent works on fractional order differential equations involving Riemann-Liouville, Caputo, and Hadamard type fractional derivatives, equipped with classical, nonlocal, and integral boundary conditions, we refer the reader to a series of papers [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] and the references cited therein.…”

Existence results for a coupled system of Caputo type sequential fractional differential equations with nonlocal integral boundary conditions

“…With this advantage, fractional-order models are regarded as more realistic and practical. For some recent development on the topic, see [5][6][7][8][9][10][11][12][13][14][15][16][17][18] and the references therein. The study of coupled systems of fractional-order differential equations is also very significant as such systems appear in a variety of problems of applied nature, especially in biosciences.…”

Existence Results for a System of Coupled Hybrid Differential Equations with Fractional Order

“…For some recent work on the topic, see [5][6][7][8][9][10][11][12] and the references therein. e study of coupled systems of fractional order differential equations is quite important as such systems appear in a variety of problems of applied nature, especially in biosciences.…”