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1
Content available On nonlinear fractional neutral differential equation with the ψ-Caputo fractional derivative
Nabil Tamer
Journal of Mathematics and Applications
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2020
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Vol. 43
99--112
EN
In this article, the solvability of fractional neutral differential equation involving ψ-Caputo fractional operator is considered usinga Krasnoselskii’s fixed point approach. Also, we establish the uniquenessof the solution under certain conditions. Ulam stabilities for the proposedproblem are discussed. Finally, examples are displayed to aid the applicability of the theory results.
2
Content available Fractional boundary value problems on the half line
Frioui A., Guezane-Lakoud A., Khaldi R.
Opuscula Mathematica
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2017
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Vol. 37, no. 2
265--280
EN
In this paper, we focus on the solvability of a fractional boundary value problem at resonance on an unbounded interval. By constructing suitable operators, we establish an existence theorem upon the coincidence degree theory of Mawhin. The obtained results are illustrated by an example.
3
On nonlinear mixed fractional integrodifferential equations with nonlocal condition in Banach spaces
Kendre S. D., Kharat V. V.
Journal of Applied Analysis
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2014
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Vol. 20, nr 2
167--175
EN
In the present paper we investigate the existence and uniqueness of solutions of nonlinear mixed fractional integrodifferential equations with nonlocal condition in Banach spaces. The technique used in our analysis is based on fixed point theorems and Pachpatte's integral inequality.
4
Content available remote Existence and uniqueness of solutions of the dirichlet nonlocal problem with nonlocal initial condition
Byszewski L., Winiarska T.
Czasopismo Techniczne. Nauki Podstawowe
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2014
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R. 111, z. 2-NP
3--7
EN
The aim of this paper is to prove the existence and uniqueness of solutions of the Dirichlet nonlocal problem with nonlocal initial condition. The considerations are extensions of results by E. Andreu-Vaillo, J. M. Mazón, J. D. Rossi and J. J. Toledo-Melero.
PL
W artykule udowodniono istnienie i jednoznaczność rozwiązań nielokalnego zagadnienia Dirichleta z nielokalnym warunkiem początkowym. Rozważania są rozszerzeniami rezultatów otrzymanych przez E. Andreu-Vaillo, J. M. Mazóna, J. D. Rossi i J. J. Toledo-Melero.
5
Some theorems on fractional semilinear evolution equations
Tidke H. L.
Journal of Applied Analysis
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2012
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Vol. 18, nr 2
209-224
EN
In this paper, we investigate the existence, uniqueness and other properties of solutions of fractional semilinear evolution equations in Banach spaces. The results are obtained by using fractional calculus, the well-known Banach fixed point theorem coupled with Bielecki type norm and the integral inequality established by E. Hernandez.
6
Content available remote Of neutral type hyperbolic integrodifferential equation
Pachpatte B. G.
Fasciculi Mathematici
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2008
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Nr 40
57-69
EN
In this paper we study the existence, uniqueness and other properties of solutions of a certain neutral type hyperbolic integrodifferential equation in two independent variables. The Banach fixed point theorem and a certain integral inequality with explicit estimate are used to establish the results.
7
Content available remote Existance of solutions of nonlinear integral equations and Henstock-Kurzweil integrals
Sikorska-Nowak A.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2007
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Vol. 47, [Z] 2
227-238
EN
We prove an existence theorems for the nonlinear integral equation... [formuła matematyczna]... where f, g, x are functions with values in Banach spaces. Our fundamental tools are: measures of noncompactness and properties of the Henstock-Kurzweil integral.
8
Content available remote Retarded functional differential equations in Banach spaces and Henstock-Kurzweil integrals
Sikorska-Nowak A.
Demonstratio Mathematica
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2002
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Vol. 35, nr 1
49-60
EN
In this paper, using properties of the Henstock-Kurzweil integral and corresponding theorems, we prove existence theorems for the equation x' = f(t,xt) and inclusion x' F(t,xt) in a Banach space where f is Henstock-Kurzweil integrable and satisfies some additional conditions.
9
Content available remote On a construction of hypoparabolic polynomials ot two spatial variables and its application
Pieniążek A.
Fasciculi Mathematici
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1999
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Nr 29
99-112
EN
The aim of the paper is to construct hypoparabolic polynomials of two spatia1 variables satisfying an hypoparabolic equation and to apply the theory of those polynomials for a finding of a solution of a initial-boundary value problem.
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