• Nonlinear Functional Analysis and Applications
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• 제29권3호
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• pp.803-823
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• 2024

In this paper, we study the existence and uniqueness of solutions for the fractional time-varying delay integrodifferential equation with multi-point multi-term nonlocal and fractional integral boundary conditions by using fixed point theorems. The fractional derivative considered here is in the Caputo sense. Examples are provided to illustrate the results.

• Nonlinear Functional Analysis and Applications
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• 제26권4호
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• pp.793-809
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• 2021

This paper gives sufficient conditions to ensure the existence and stability of solutions for generalized nonlinear fractional integrodifferential equations of order α (1 < α < 2). The main theorem asserts the stability results in a weighted Banach space, employing the Krasnoselskii's fixed point technique and the existence of at least one mild solution satisfying the asymptotic stability condition. Two examples are provided to illustrate the theory.

• Journal of applied mathematics & informatics
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• 제40권5_6호
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• pp.1089-1103
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• 2022

This paper focuses on the existence and uniqueness outcome for fractional integro-differential equation (FIDE) among impulsive edge condition and Hyers-Ulam-Rassias Stability (HURS) by using fractional calculus and some fixed point theorem in some weak conditions. The outcome procured in this paper upgrade and perpetuate some studied solutions.

• 대한수학회보
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• 제46권4호
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• pp.691-700
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• 2009

We prove the local existence of classical solutions of quasi-linear integrodifferential equations in Banach spaces. The results are obtained by using fractional powers of operators and the Schauder fixed-point theorem. An example is provided to illustrate the theory.

• 충청수학회지
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• 제27권1호
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• pp.89-97
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• 2014

We study the existence of mild solutions for neutral differential equations with nonlocal conditions in the ${\alpha}$-norm.