• Nonlinear Functional Analysis and Applications
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• 제28권2호
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• pp.449-471
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• 2023

In this paper, we study a linear system of homogeneous commensurate /incommensurate fractional-order differential equations by developing a new semi-analytical scheme. In particular, by decoupling the system into two fractional-order differential equations, so that the first equation of order (δ + γ), while the second equation depends on the solution for the first equation, we have solved the under consideration system, where 0 < δ, γ ≤ 1. With the help of using the Adomian decomposition method (ADM), we obtain the general solution. The efficiency of this method is verified by solving several numerical examples.

• Nonlinear Functional Analysis and Applications
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• 제28권3호
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• pp.851-863
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• 2023

We study the appropriate conditions for the findings of uniqueness and existence for a group of boundary value problems for impulsive Ψ-Caputo fractional nonlinear Volterra-Fredholm integro-differential equations (V-FIDEs) with symmetric boundary non-instantaneous conditions in this paper. The findings are based on the fixed point theorem of Krasnoselskii and the Banach contraction principle. Finally, the application is provided to validate our primary findings.

• Nonlinear Functional Analysis and Applications
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• 제28권2호
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• pp.365-382
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• 2023

In this paper we prove the existence and uniqueness of solution of stochastic fractional neutral differential equations with Gaussian noise or Lévy noise by using the Picard-Lindelöf successive approximation scheme. Further stability results of nonlinear stochastic fractional dynamical system with Gaussian and Lévy noises are established. Examples are provided to illustrate the theoretical results.

• East Asian mathematical journal
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• 제30권5호
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• pp.631-637
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• 2014

In this paper, we construct some results on the existence and regularity for solutions of neutral functional differential equations with unbounded principal operators in Hilbert spaces. In order to establish the existence and regularity for solutions of the neutral system by using fractional power of operators and the local Lipschtiz continuity of nonlinear term without using many of the strong restrictions considering in the previous literature.

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.259-273
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• 2024

In this manuscript, we study the sufficient conditions for existence and uniqueness results of solutions of impulsive Hilfer fractional Volterra-Fredholm integro-differential equations with integral boundary conditions. Fractional calculus and Banach contraction theorem used to prove the uniqueness of results. Moreover, we also establish Hyers-Ulam stability for this problem. An example is also presented at the end.

• 대한수학회지
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• 제55권5호
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• pp.1269-1283
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• 2018

We are concerned with elliptic equations in ${\mathbb{R}}^N$, driven by a non-local integro-differential operator, which involves the fractional Laplacian. The main aim of this paper is to prove the existence of small solutions for our problem with negative energy in the sense that the sequence of solutions converges to 0 in the $L^{\infty}$-norm by employing the regularity type result on the $L^{\infty}$-boundedness of solutions and the modified functional method.

• Nonlinear Functional Analysis and Applications
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• 제29권2호
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• pp.501-515
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• 2024

The primary focus of this paper is to thoroughly examine and analyze a coupled system by a Hilfer-Hadamard-type fractional differential equation with coupled boundary conditions. To achieve this, we introduce an operator that possesses fixed points corresponding to the solutions of the problem, effectively transforming the given system into an equivalent fixed-point problem. The necessary conditions for the existence and uniqueness of solutions for the system are established using Banach's fixed point theorem and Schaefer's fixed point theorem. An illustrate example is presented to demonstrate the effectiveness of the developed controllability results.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제15권3호
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• pp.245-257
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• 2008

In this paper, we find the sufficient conditions of controllability of semi-linear neutral functional differential evolution equations with non local conditions using by fractional power of operators and Sadovskii's fixed point theorem.

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.113-130
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• 2024

In this work, we explore the existence and uniqueness results for a class of boundary value issues for implicit Volterra-Fredholm nonlinear integro-differential equations (IDEs) with Atangana-Baleanu-Riemann fractional (ABR-fractional) that have non-instantaneous multi-point fractional boundary conditions. The findings are supported by Krasnoselskii's fixed point theorem, Gronwall-Bellman inequality, and the Banach contraction principle. Finally, a demonstrative example is provided to support our key findings.

• 충청수학회지
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• 제31권2호
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• pp.255-268
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• 2018

We establish the existence and multiplicity of positive solutions to a coupled system of fractional order differential equations satisfying three-point boundary conditions by utilizing Avery-Henderson functional fixed point theorems and under suitable conditions.