4.6 Article

Existence of solutions for Caputo fractional iterative equations under several boundary value conditions

Related references

Note: Only part of the references are listed.
Article Mathematics, Applied

On the nonlinear Ψ-Hilfer hybrid fractional differential equations

Kishor D. Kucche et al.

Summary: In this paper, the equivalent fractional integral equation is derived and used to prove the existence of a solution in the weighted space for Psi-Hilfer hybrid fractional differential equations. The primary objective is to obtain estimates on Psi-Hilfer fractional derivative and utilize it to derive hybrid fractional differential inequalities involving Psi Hilfer fractional derivative. With the help of these differential inequalities, the existence of extremal solutions and comparison theorems are determined.

COMPUTATIONAL & APPLIED MATHEMATICS (2022)

Article Multidisciplinary Sciences

The Existence and Uniqueness of Solution to Sequential Fractional Differential Equation with Affine Periodic Boundary Value Conditions

Shanshan Gao et al.

Summary: This paper investigates the solution to a sequential fractional differential equation with affine periodic boundary value conditions. The existence theorem of solution is established using the Leray-Schauder fixed point theorem and Krasnoselskii fixed point theorem. Furthermore, the uniqueness theorem of solution is demonstrated via Banach contraction mapping principle. Two examples are provided to illustrate the main results.

SYMMETRY-BASEL (2022)

Article Mathematics, Interdisciplinary Applications

Extremal Solutions of Generalized Caputo-Type Fractional-Order Boundary Value Problems Using Monotone Iterative Method

Choukri Derbazi et al.

Summary: The aim of this research is to derive extremal solutions for a class of generalized Caputo-type nonlinear fractional differential equations under nonlinear boundary conditions. The results are obtained using the monotone iterative method, which generates two sequences of extremal solutions converging to the upper and lower solutions respectively. This method does not require any prior discretization or collocation, and produces a fruitful combination of upper and lower solutions.

FRACTAL AND FRACTIONAL (2022)

Article Mathematics, Interdisciplinary Applications

Results on system of Atangana-Baleanu fractional order Willis aneurysm and nonlinear singularly perturb ed boundary value problems

Sumati Kumari Panda et al.

Summary: This article discusses the initiation of solutions using fixed point technique for the Atangana-Baleanu Willis Aneurysm System and singular perturbations of boundary value problems for non-linear fuzzy differential equations of the second order, analyzing the equations and conditions of the two problems.

CHAOS SOLITONS & FRACTALS (2021)

Article Mathematics, Applied

An existence result for an infinite system of implicit fractional integral equations via generalized Darbo's fixed point theorem

Anupam Das et al.

Summary: In this article, we extend Darbo's fixed point theorem and use it to prove the existence of solutions for an infinite system of implicit fractional integral equations. The proposed fixed point theory relaxes the requirement of compactness of the domain, which is essential in some fixed point theorems. Additionally, we apply it to integral equations involving fractional integrals, which generalizes many fixed point theorems and fractional integral equations.

COMPUTATIONAL & APPLIED MATHEMATICS (2021)

Article Multidisciplinary Sciences

Existence of Solutions for a Singular Fractional q-Differential Equations under Riemann-Liouville Integral Boundary Condition

Mohammad Esmael Samei et al.

Summary: In this work, we investigate the existence of solutions for a system of m-singular sum fractional q-differential equations under integral boundary conditions in the sense of Caputo fractional q-derivatives. Utilizing a fixed point Arzela-Ascoli theorem, we establish the existence of positive solutions. By presenting examples with graphs, tables, and algorithms, our fundamental result regarding the endpoint is illustrated with given computational results. Furthermore, a common correlation between symmetry and q-difference equations is noted, suggesting that q-deformations in Lie algebra can be constructed with the aid of symmetry concepts.

SYMMETRY-BASEL (2021)

Article Mathematics, Interdisciplinary Applications

Monotone Iterative and Upper-Lower Solution Techniques for Solving the Nonlinear ψ-Caputo Fractional Boundary Value Problem

Abdelatif Boutiara et al.

Summary: The paper studies the existence of extremal solutions for nonlinear boundary value problems of fractional differential equations, obtaining main results through the monotone iterative technique combined with upper and lower solutions. It examines three cases for psi*(t) as t, Caputo, 2t, t, and Katugampola derivatives, validating the acquired outcomes with the help of two different particular examples.

FRACTAL AND FRACTIONAL (2021)

Article Mathematics, Interdisciplinary Applications

A Mathematical Study of a Coronavirus Model with the Caputo Fractional-Order Derivative

Youcef Belgaid et al.

Summary: In this study, a minimal model for the current pandemic was introduced, incorporating basic compartments and formulated using fractional operators. The analysis of model equilibria showed that the stability behavior is similar to systems formulated with standard derivatives, indicating that memory effects in fractional operators may not be significant in this case. However, numerical simulations demonstrated that the order of the fractional derivative does have a definite influence on equilibrium population levels and the speed of attainment.

FRACTAL AND FRACTIONAL (2021)

Article Mathematics, Applied

Rotational periodic solutions for fractional iterative systems

Rui Wu et al.

Summary: This paper focuses on the rotational periodic problem of fractional iterative systems under Caputo fractional derivative. By proving the existence and uniqueness of solutions using Leray-Schauder fixed point theorem and topological degree theory, as well as demonstrating the existence of solutions for a control system and a neural network system, the study showcases the well posedness of these systems.

AIMS MATHEMATICS (2021)

Article Mathematics

Rotating periodic integrable solutions for second-order differential systems with nonresonance condition

Yi CHENG et al.

Summary: This paper proves the existence and uniqueness of rotating periodic integrable solution for the second-order system when the nonlinearity satisfies nonresonance condition.

TURKISH JOURNAL OF MATHEMATICS (2021)

Article Engineering, Multidisciplinary

Novel fixed point approach to Atangana-Baleanu fractional and Lp-Fredholm integral equations

Sumati Kumari Panda et al.

ALEXANDRIA ENGINEERING JOURNAL (2020)

Article Mathematics, Applied

Solutions of boundary value problems on extended-Branciari b-distance

Thabet Abdeljawad et al.

JOURNAL OF INEQUALITIES AND APPLICATIONS (2020)

Article Mathematics, Applied

On p-Laplacian boundary value problems involving Caputo-Katugampula fractional derivatives

Mohammed M. Matar et al.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES (2020)

Article Mathematics, Applied

Rotational periodic boundary value problem for a fractional nonlinear differential equation

Yi Cheng et al.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES (2020)

Article Mathematics

Solvability of Fractional Multi-Point Boundary Value Problems with Nonlinear Growth at Resonance

Zidane Baitiche et al.

JOURNAL OF CONTEMPORARY MATHEMATICAL ANALYSIS-ARMENIAN ACADEMY OF SCIENCES (2020)

Article Mathematics

Periodic solutions of a class of third-order functional differential equations with iterative source terms

Ahleme Bouakkaz et al.

BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA (2020)

Article Mathematics

Existence of periodic solutions for nonlinear implicit Hadamard's fractional differential equations

Mouffak Benchohra et al.

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS (2018)

Article Mathematics, Applied

Periodic solutions of an iterative functional differential equation with variable coefficients

Hou Yu Zhao et al.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES (2017)

Article Mathematics, Applied

Iterative technique for a third-order differential equation with three-point nonlinear boundary value conditions

Xiuli Lin et al.

ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS (2016)

Article Mathematics, Applied

Global Mittag-Leffler projective synchronization for fractional-order neural networks: an LMI-based approach

Huaiqin Wu et al.

ADVANCES IN DIFFERENCE EQUATIONS (2016)

Article Mathematics, Applied

Existence and uniqueness for a class of iterative fractional differential equations

Rabha W. Ibrahim et al.

ADVANCES IN DIFFERENCE EQUATIONS (2015)

Article Computer Science, Artificial Intelligence

Global Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks

Jiejie Chen et al.

NEURAL NETWORKS (2014)

Article Mathematics, Applied

Application of measure of noncompactness to a Cauchy problem for fractional differential equations in Banach spaces

Asadollah Aghajani et al.

FRACTIONAL CALCULUS AND APPLIED ANALYSIS (2013)

Article Mathematics, Applied

Anti-periodic solutions for nonlinear evolution equations

Yi Cheng et al.

ADVANCES IN DIFFERENCE EQUATIONS (2012)

Article Mathematics, Applied

A generalized Gronwall inequality and its application to a fractional differential equation

Haiping Ye et al.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2007)