Existence of at Least Three Distinct Weak Solutions for a Class of Nonlinear System of Fractional Differential Equations

This paper deals with the existence of solutions for a new class of nonlinear fractional boundary value systems involving the left and right Riemann-Liouville fractional derivatives. More precisely, we establish the existence of at least three weak solutions for the problem using variational methods combined with the critical point theorem due to Bonano and Marano. In addition, some examples in ℝ 3 and ℝ 4 are given to illustrate the theoritical results.

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Two-point nonlocal nonlinear fractional boundary value problem with Caputo derivative: Analysis and numerical solution

AhmadSoltani

2022

Nonlinear Engineering

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This work presents the existential and unique results for the solution to a kind of high-order fractional nonlinear differential equations involving Caputo fractional derivative. The boundary condition is of the integral type, which entangles both starting and ending points of the domain. First, the unique exact solution is extracted in terms of Green’s function for the linear fractional differential equation, and then Banach contraction mapping theorem is applied to prove the main result in the case of the general nonlinear source term. Then, our main result is demonstrated by an illustrative example, which shows its legitimacy and applicability. Furthermore, numerical-based semi-analytical technique has been presented to approximate the unique solution to the desired order of precision.

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Existence of at Least Three Distinct Weak Solutions for a Class of Nonlinear System of Fractional Differential Equations

Cited by 3 publications

References 26 publications

A unique weak solution for the fractional integro-differential schrödinger equations

A unique weak solution for the fractional integro-differential schrödinger equations

On Existence of Multiplicity of Weak Solutions for a New Class of Nonlinear Fractional Boundary Value Systems via Variational Approach

Two-point nonlocal nonlinear fractional boundary value problem with Caputo derivative: Analysis and numerical solution

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