Existence and uniqueness of solutions for a coupled system of nonlinear fractional differential equations with fractional integral boundary conditions

Zhang, Haiyan; Li, Yaohong; Wei, Lu

doi:10.22436/jnsa.009.05.43

Cited by 12 publications

(6 citation statements)

References 26 publications

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“…For more details on the FC, one can see [17,23,24]. In fact, many researchers have devoted themselves to investigate fractional order differential equations and systems with different boundary conditions, for more details, the reader can see the works [1,3,4,6,9,10,14,20,22,29,[37][38][39]41].…”

Section: Introductionmentioning

confidence: 99%

Beam deflection coupled systems of fractional differential equations: existence of solutions, Ulam–Hyers stability and travelling waves

Bensassa,

Dahmani,

Rakah

et al. 2024

Anal.Math.Phys.

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In this paper, we study a coupled system of beam deflection type that involves nonlinear equations with sequential Caputo fractional derivatives. Under flexible/fixed end-conditions, two main theorems on the existence and uniqueness of solutions are proved by using two fixed point theorems. Some examples are discussed to illustrate the applications of the existence and uniqueness of solution results. Another main result on the Ulam–Hyers stability of solutions for the introduced system is also discussed. Some examples of stability are discussed. New travelling wave solutions are obtained for another conformable coupled system of beam type that has a connection with the first considered system. A conclusion follows at the end.

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Section: Introductionmentioning

confidence: 99%

Beam deflection coupled systems of fractional differential equations: existence of solutions, Ulam–Hyers stability and travelling waves

Bensassa,

Dahmani,

Rakah

et al. 2024

Anal.Math.Phys.

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“…In recent years, Caputo and Fabrizio introduced a new operator with a nonsingular kernel known as the Caputo-Fabrizio operator [4]. A large number of papers have recently been published dealing with the existence of solutions to nonlinear fractional differential equations using nonlinear analysis techniques [5][6][7][8][9][10][11][12][13]. Also, many researchers used the new definitions of fractional derivative and integral Caputo-Fabrizio to solve several fractional differential equations [14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

The nonlocal coupled system of Caputo–Fabrizio fractional q‐integro differential equation

Ali,

Raslan,

Ibrahim

et al. 2023

Math Methods in App Sciences

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This scheme's main goal is to examine the existence, uniqueness, and continuous dependence of solutions for a nonlinear coupled system of fractional q‐integro‐differential equations involving the derivation and integration of fractional Caputo–Fabrizio. The numerical technique methodology of the proposed problem will be introduced. Proving the existence theorem depends on Schauder's fixed‐point theorem. To drive the numerical method, we use the definitions of the fractional derivative and integral of Caputo–Fabrizio and the q‐integral of the Riemann–Liouville type. Then, the integral part will be treated using the trapezoidal method, and the derivative part will be treated using the forward finite difference method. And therefore, the coupled system will be converted into a system of algebraic equation that will be solved together to get the solutions. Finally, we give two examples to illustrate the effectiveness of the suggested approach.

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“…Meanwhile, there are a lot of papers (see [3,[17][18][19][20][21][22][23][24][25][26][27][28], for instance) dealing with the existence of positive solutions of nonlinear fractional differential equations by use of fixedpoint theorems, monotone iterative technique, and upper and lower solution method. For example, in [25], by using the method of upper and lower solutions and Schauder fixed theorem, Vong investigated the positive solutions for the following nonlocal fractional BVP:…”

Section: Introductionmentioning

confidence: 99%

Multiple Positive Solutions for Nonlinear Fractional Differential Equations with Integral Boundary Value Conditions and a Parameter

Mao

Deng-feng

2019

Journal of Function Spaces

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By using the theory of fixed-point index on cone for differentiable operators, spectral radii of some related linear integral operators, and properties of Green’s function, the existence of multiple positive solutions to a nonlinear fractional differential system with integral boundary value conditions and a parameter is established. At last, some examples are also provided to illustrate the validity of our main results.

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Existence and uniqueness of solutions for a coupled system of nonlinear fractional differential equations with fractional integral boundary conditions

Cited by 12 publications

References 26 publications

Beam deflection coupled systems of fractional differential equations: existence of solutions, Ulam–Hyers stability and travelling waves

Beam deflection coupled systems of fractional differential equations: existence of solutions, Ulam–Hyers stability and travelling waves

The nonlocal coupled system of Caputo–Fabrizio fractional q‐integro differential equation

Multiple Positive Solutions for Nonlinear Fractional Differential Equations with Integral Boundary Value Conditions and a Parameter

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