Uniqueness of Solutions, Stability and Simulations for a Differential Problem Involving Convergent Series and Time Variable Singularities

We focus on a new type of nonlinear integro-differential equations with nonlocal integral conditions. The considered problem has one nonlinearity with time variable singularity. It involves also some convergent series combined to Riemann-Liouville integrals. We prove a uniqueness of solutions for the proposed problem, then, we provide some examples to illustrate this result. Also, we discuss the Ulam-Hyers stability for the problem. Some numerical simulations, using Rung Kutta method, are discussed too. At the end, a conclusion follows.

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System of fractional differential equations with Erdélyi-Kober fractional integral conditions

Open Mathematics ◽

10.1515/math-2015-0079 ◽

2015 ◽

Vol 13 (1) ◽

Cited By ~ 1

Author(s):

Natthaphong Thongsalee ◽

Sorasak Laoprasittichok ◽

Sotiris K. Ntouyas ◽

Jessada Tariboon

Keyword(s):

Differential Equations ◽

Fractional Differential Equations ◽

Existence And Uniqueness ◽

Fractional Integral ◽

Existence Of Solutions ◽

Integral Conditions ◽

Liouville Type ◽

Uniqueness Of Solutions ◽

Fractional Differential ◽

Banach’S Contraction Principle

AbstractIn this paper we study existence and uniqueness of solutions for a system consisting from fractional differential equations of Riemann-Liouville type subject to nonlocal Erdélyi-Kober fractional integral conditions. The existence and uniqueness of solutions is established by Banach’s contraction principle, while the existence of solutions is derived by using Leray-Schauder’s alternative. Examples illustrating our results are also presented.

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Singular integro-differential equations with applications

Evolution Equations and Control Theory ◽

10.3934/eect.2021051 ◽

2021 ◽

Vol 0 (0) ◽

pp. 0

Author(s):

Mohammed Al Horani ◽

Angelo Favini ◽

Hiroki Tanabe

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Existence And Uniqueness ◽

Uniqueness Of Solutions ◽

Partial Differential ◽

Differential Problem

<p style='text-indent:20px;'>We are devoted with singular integro-differential abstract Cauchyproblems. Required conditions on spaces and operators are givenguaranteeing existence and uniqueness of solutions. Applications from partial differential equations are given to illustrate the abstract singular integro-differential problem.</p>

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Existence of solutions of boundary value problems for nonlinear fractional differential equations with integral conditions

Proyecciones (Antofagasta) ◽

10.22199/issn.0717-6279-4271 ◽

2021 ◽

Vol 40 (5) ◽

pp. 1117-1135

Author(s):

Ahcene Boukehila

Keyword(s):

Differential Equations ◽

Fractional Derivative ◽

Boundary Value Problems ◽

Fractional Differential Equations ◽

Nonlinear Term ◽

Boundary Value ◽

Integral Conditions ◽

Uniqueness Of Solutions ◽

Banach Contraction ◽

Fractional Differential

In this work we investigate the existence and uniqueness of solutions of boundary value problems for fractional differential equations involving the Caputo fractional derivative with integral conditions and the nonlinear term depends on the fractional derivative of an unknown function. Our existence results are based on Banach contraction principle and Schauder fixed point theorem. Two examples are provided to illustrate our results.

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Unpredictable Solutions of Linear Impulsive Systems

Mathematics ◽

10.3390/math8101798 ◽

2020 ◽

Vol 8 (10) ◽

pp. 1798

Author(s):

Marat Akhmet ◽

Madina Tleubergenova ◽

Mehmet Onur Fen ◽

Zakhira Nugayeva

Keyword(s):

Differential Equations ◽

Numerical Simulations ◽

Random Process ◽

Logistic Map ◽

Impulsive Differential Equations ◽

Impulsive Systems ◽

New Type ◽

Piecewise Continuous ◽

Definition Of ◽

Theoretical Results

We consider a new type of oscillations of discontinuous unpredictable solutions for linear impulsive nonhomogeneous systems. The models under investigation are with unpredictable perturbations. The definition of a piecewise continuous unpredictable function is provided. The moments of impulses constitute a newly determined unpredictable discrete set. Theoretical results on the existence, uniqueness, and stability of discontinuous unpredictable solutions for linear impulsive differential equations are provided. We benefit from the B-topology in the space of discontinuous functions on the purpose of proving the presence of unpredictable solutions. For constructive definitions of unpredictable components in examples, randomly determined unpredictable sequences are newly utilized. Namely, the construction of a discontinuous unpredictable function is based on an unpredictable sequence determined by a discrete random process, and the set of discontinuity moments is realized by the logistic map. Examples with numerical simulations are presented to illustrate the theoretical results.

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Theoretical and experimental research on slip and uplift of the timber-concrete composite beam

BioResources ◽

10.15376/biores.15.3.7079-7099 ◽

2020 ◽

Vol 15 (3) ◽

pp. 7079-7099

Author(s):

Jianying Chen ◽

Guojing He ◽

Xiaodong (Alice) Wang ◽

Jiejun Wang ◽

Jin Yi ◽

...

Keyword(s):

Differential Equations ◽

Deformation Theory ◽

Concrete Slab ◽

Theoretical Calculations ◽

Structural Element ◽

Structural Efficiency ◽

Theoretical Investigations ◽

New Type ◽

Interlayer Slip ◽

Good Agreement

Timber-concrete composite beams are a new type of structural element that is environmentally friendly. The structural efficiency of this kind of beam highly depends on the stiffness of the interlayer connection. The structural efficiency of the composite was evaluated by experimental and theoretical investigations performed on the relative horizontal slip and vertical uplift along the interlayer between composite’s timber and concrete slab. Differential equations were established based on a theoretical analysis of combination effects of interlayer slip and vertical uplift, by using deformation theory of elastics. Subsequently, the differential equations were solved and the magnitude of uplift force at the interlayer was obtained. It was concluded that the theoretical calculations were in good agreement with the results of experimentation.

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