A nonlinear fractional partial integro‐differential equation with nonlocal initial value conditions

Li, Chenkuan; Saadati, Reza; O’Regan, Donal; Mesiar, Radko; Hrytsenko, Andriy

doi:10.1002/mma.9486

Cited by 2 publications

(1 citation statement)

References 18 publications

(19 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recently, there has been a significant rise in attention towards fractional order differential equations with multi-point boundary values. When compared to two-point boundary value problems, the advantage of different equations in multi-point boundary value problems is that they can be used as a framework for describing many real-world problems, with the meaning being expressed more clearly and accurately [3]. Furthermore, the multipoint boundary value problem of differential equations has a broader practical application background in the signaling and aerospace fields.…”

Section: Introductionmentioning

confidence: 99%

A study of the multipoint boundary value problem for nonlinear differential equations of arbitrary fractional order based on the fixed point theorem for composite nonlinear operators

Luo

2024

Applied Mathematics and Nonlinear Sciences

View full text Add to dashboard Cite

The existence and distinctiveness of solutions, as well as the iterative approximations of the distinctive answer to the initial boundary value issue of nonlinear differential equations, may be solved with the help of the theory of nonlinear operators, which offers a strong theoretical guarantee and a fundamental tool. In this work, we examine the fixed point theory for composites nonlinear operators, which may offer a fresh approach to solving linear differential equations having arbitrary order fractional multipoint boundary value problems. The existing result of the boundary value issue’s solution is confirmed by the fixed point theorem for composites nonlinear operators, and the four-point boundary value problem for fractional-order linear equations of the Riemann-Liouville type is examined. A group of fractional-order nonlinear differential equations with deviating quantities are examined to examine the presence of an unusual positive solution for this boundary value problem. The existence of this unique positive solution is determined by the use of both the mixed monotone operator and the combined nonlinear operator fixed point theorem. Ultimately, the nonlinear Bagley-Torvik equation with a fractional order variable coefficient four-point boundary value problem is converted into a Fredholm-Hammerstein integral the formula of the second type with weakly singular or continuous kernels, and the fixed point principle is used to demonstrate the uniqueness of the solution in the space of continuous functions. Approximate solutions are provided for the second class of nonlinear Fredholm-Hammerstein integral equations with weakly singular kernels. The outcomes demonstrate the applicability and validity of the fixed point theorem to composite nonlinear operators, offering a fresh approach to solving the multipoint boundary value issue for nonlinear differential equations of any fractional order.

show abstract

Section: Introductionmentioning

confidence: 99%

A study of the multipoint boundary value problem for nonlinear differential equations of arbitrary fractional order based on the fixed point theorem for composite nonlinear operators

Luo

2024

Applied Mathematics and Nonlinear Sciences

View full text Add to dashboard Cite

show abstract

Uniqueness and Hyers–Ulam’s stability for a fractional nonlinear partial integro-differential equation with variable coefficients and a mixed boundary condition

2024

Can. J. Math.-J. Can. Math.

Self Cite

View full text Add to dashboard Cite

Introducing a pair-parameter matrix Mittag–Leffler function, we study the uniqueness and Hyers–Ulam stability to a new fractional nonlinear partial integro-differential equation with variable coefficients and a mixed boundary condition using Banach’s contractive principle as well as Babenko’s approach in a Banach space. These investigations have serious applications since uniqueness and stability analysis are essential topics in various research fields. The techniques used also work for different types of differential equations with initial or boundary conditions, as well as integral equations. Moreover, we present a Python code to compute approximate values of our newly established pair-parameter matrix Mittag–Leffler functions, which extend the multivariate Mittag–Leffler function. A few examples are given to show applications of the key results obtained.

show abstract

A nonlinear fractional partial integro‐differential equation with nonlocal initial value conditions

Cited by 2 publications

References 18 publications

A study of the multipoint boundary value problem for nonlinear differential equations of arbitrary fractional order based on the fixed point theorem for composite nonlinear operators

A study of the multipoint boundary value problem for nonlinear differential equations of arbitrary fractional order based on the fixed point theorem for composite nonlinear operators

Uniqueness and Hyers–Ulam’s stability for a fractional nonlinear partial integro-differential equation with variable coefficients and a mixed boundary condition

Contact Info

Product

Resources

About