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Almost-periodicity in linear topological spaces and applications to abstract differential equations [PDF]
International Journal of Mathematics and Mathematical Sciences, 1984 Let E be a complete locally convex space (l.c.s.) and f:R→E a continuous function; then f is said to be almost-periodic (a.p.) if, for every neighbourhood (of the origin in E) U, there exists ℓ=ℓ(U)>0 such that every interval [a,a+ℓ] of the real line ...
Gaston Mandata N'Guerekata
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Approximation of inverse problems for fractional differential equations in abstract spaces
Alexandria Engineering JournalThis article focuses on approximating a fractional-order inverse problem (IP) for an abstract differential equation in a Hilbert space. The main tools to find out the results are fixed-point methods, the α-resolvent family, and optimal control (OC ...
Santosh Ruhil +3 more
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Differential inclusions of arbitrary fractional order with anti-periodic conditions in Banach spaces [PDF]
, 2016 In this paper, we establish various existence results of solutions for fractional differential equations and inclusions of arbitrary order $q\in (m-1,m)$, where $m$ is an arbitrary natural number greater than or equal to two, in infinite dimensional ...
Feckan, Michal +2 more
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Journal of Inequalities and Applications, 2023 A novel measure of noncompactness is defined in variable exponent Lebesgue spaces L p ( ⋅ ) $L^{p(\cdot )}$ on an unbounded domain R + $\mathbb{R}^{+}$ and its properties are examined.
Mohamed M. A. Metwali
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Fixed Point Theory and Algorithms for Sciences and Engineering, 2022 In this article, we present an approach to solve a wide range of nonlinear equations formulated in extended b-metric spaces based on a new fixed-point theorem on these spaces.
Abdelkader Belhenniche +3 more
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ON DISCONTINUOUS FUNCTIONAL VOLTERRA INTEGRAL EQUATIONS AND IMPULSIVE DIFFERENTIAL EQUATIONS IN ABSTRACT SPACES [PDF]
Glasgow Mathematical Journal, 2004 In this paper we apply fixed point results in ordered spaces to derive existence and comparison results for discontinuous functional integral equations of Volterra type in ordered Banach spaces. The results obtained are then applied to first order impulsive differential equations.
HEIKKILÄ, S., O'REGAN, D.
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Best proximity point results and application to a system of integro-differential equations
Advances in Difference Equations, 2021 In this work, we solve the system of integro-differential equations (in terms of Caputo–Fabrizio calculus) using the concepts of the best proximity pair (point) and measure of noncompactness.
Anupam Das +3 more
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Inequalities for integral operators in Hölder–Morrey spaces on differential forms
Journal of Inequalities and Applications, 2023 The Hölder–Morrey spaces Λ κ p , τ ( Ω , ∧ l ) $\Lambda _{\kappa}^{p,\tau}(\Omega ,\wedge ^{l})$ are proposed in this paper. The imbedding inequalities for homotopy operator are derived in Hölder–Morrey spaces on differential forms. The Hölder continuity
Xuexin Li, Jianwei Wang, Ning Pan
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Alexandria Engineering Journal, 2023 This article aims to study the existence of the solutions to the infinite system of Hilfer fractional differential equations in tempered sequence spaces.
Inzamamul Haque +2 more
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Relations between stochastic and partial differential equations in hilbert spaces [PDF]
, 2012 The aim of the paper is to introduce a generalization of the Feynman-Kac theorem in Hilbert spaces. Connection between solutions to the abstract stochastic differential equation d X (t) = A X (t) d t + B d W (t) and solutions to the deterministic partial
Melnikova, I. V., Parfenenkova, V. S.
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