scholarly journals Uniqueness of the solution of the boundary-initial value problem for a linear elastic Cosserat continuum

1971 ◽  
Vol 16 (6) ◽  
pp. 402-411
Author(s):  
Miroslav Hlaváček
Keyword(s):  
Initial Value Problem ◽  
Cosserat Continuum ◽  
Initial Value ◽  
Linear Elastic ◽  
Uniqueness Of The Solution

scholarly journals On a Hilfer Type Fractional Differential Equation with Nonlinear Right-Hand Side

2021 ◽  
Vol 103 (3) ◽  
pp. 140-155
Author(s):  
T. K. Yuldashev ◽  
◽  
B. J. Kadirkulov ◽  
A. R. Marakhimov ◽  
◽  
...  
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Initial Value Problem ◽  
Integral Transformation ◽  
Numerical Realization ◽  
Initial Value ◽  
Volterra Type ◽  
Fractional Integral Equation ◽  
Uniqueness Of The Solution ◽  
Fractional Differential

In this article we consider the questions of one-valued solvability and numerical realization of initial value problem for a nonlinear Hilfer type fractional differential equation with maxima. By the aid of uncomplicated integral transformation based on Dirichlet formula, this initial value problem is reduced to the nonlinear Volterra type fractional integral equation. The theorem of existence and uniqueness of the solution of given initial value problem in the segment under consideration is proved. For numerical realization of solution the generalized Jacobi–Galerkin method is applied. Illustrative examples are provided.

scholarly journals Abstract Evolution Equations of Parabolic Type in Banach and Hilbert Spaces

1961 ◽  
Vol 19 ◽  
pp. 93-125 ◽  
Author(s):  
Tosio Kato
Keyword(s):  
Evolution Equation ◽  
Hilbert Spaces ◽  
Initial Value Problem ◽  
Evolution Equations ◽  
Parabolic Type ◽  
Initial Value ◽  
Abstract Evolution Equations ◽  
Uniqueness Of The Solution

The object of the present paper is to prove some theorems concerning the existence and the uniqueness of the solution of the initial value problem for the evolution equation(E).

scholarly journals On Solvability of an Initial Value Problem for Hilfer type Fractional Differential Equation with Nonlinear Maxima

2020 ◽  
pp. 48-65
Author(s):  
T.K. Yuldashev ◽  
B.J. Kadirkulov
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Initial Value Problem ◽  
Integral Transformation ◽  
Initial Value ◽  
Volterra Type ◽  
Fractional Integral Equation ◽  
Uniqueness Of The Solution ◽  
Fractional Differential ◽  
The Stability

In this article we consider the questions of one-valued solvability of initial value problem for a nonlinear Hilfer type fractional differential equation with nonlinear maxima. By the aid of uncomplicated integral transformation based on Dirichlet formula, this initial value problem is reduced to the nonlinear Volterra type fractional integral equation with nonlinear maxima. It is proved the theorem of existence and uniqueness of the solution of given initial value problem in an interval under consideration. It is proved also the stability of the desired solution with respect to given parameter.

scholarly journals On fuzzy Volterra-Fredholm integrodifferential equation associated with Hilfer-generalized proportional fractional derivative

2021 ◽  
Vol 6 (10) ◽  
pp. 10920-10946
Author(s):  
Saima Rashid ◽  
◽  
Fahd Jarad ◽  
Khadijah M. Abualnaja ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fractional Derivative ◽  
Integrodifferential Equation ◽  
Initial Value Problem ◽  
Initial Conditions ◽  
Equivalent Form ◽  
Initial Value ◽  
Uniqueness Of The Solution ◽  
Generalized Lipschitz Condition ◽  
Fuzzy Framework

<abstract><p>This investigation communicates with an initial value problem (IVP) of Hilfer-generalized proportional fractional ($ \mathcal{GPF} $) differential equations in the fuzzy framework is deliberated. By means of the Hilfer-$ \mathcal{GPF} $ operator, we employ the methodology of successive approximation under the generalized Lipschitz condition. Based on the proposed derivative, the fractional Volterra-Fredholm integrodifferential equations $ (\mathcal{FVFIE}s) $ via generalized fuzzy Hilfer-$ \mathcal{GPF} $ Hukuhara differentiability ($ \mathcal{HD} $) having fuzzy initial conditions are investigated. Moreover, the existence of the solution is proposed by employing the fixed-point formulation. The uniqueness of the solution is verified. Furthermore, we derived the equivalent form of fuzzy $ \mathcal{FVFIE}s $ which is supposed to demonstrate the convergence of this group of equations. Two appropriate examples are presented for illustrative purposes.</p></abstract>

scholarly journals Oscillation Criteria of Singular Initial-Value Problem for Second Order Nonlinear Dynamic Equation on Time Scales

2018 ◽  
Vol 5 (1) ◽  
pp. 102-112 ◽  
Author(s):  
Shekhar Singh Negi ◽  
Syed Abbas ◽  
Muslim Malik
Keyword(s):  
Time Scales ◽  
Initial Value Problem ◽  
Dynamic Equation ◽  
Nonlinear Dynamic ◽  
Type Inequality ◽  
Second Order ◽  
Oscillation Criterion ◽  
Initial Value ◽  
Nonlinear Dynamic Equation ◽  
Singular Initial Value Problem

AbstractBy using of generalized Opial’s type inequality on time scales, a new oscillation criterion is given for a singular initial-value problem of second-order dynamic equation on time scales. Some oscillatory results of its generalizations are also presented. Example with various time scales is given to illustrate the analytical findings.

scholarly journals A Neural Network Technique for the Derivation of Runge-Kutta Pairs Adjusted for Scalar Autonomous Problems

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1842
Author(s):  
Vladislav N. Kovalnogov ◽  
Ruslan V. Fedorov ◽  
Yuri A. Khakhalev ◽  
Theodore E. Simos ◽  
Charalampos Tsitouras
Keyword(s):  
Neural Network ◽  
Differential Evolution ◽  
Initial Value Problem ◽  
Fitness Function ◽  
Initial Value ◽  
Runge Kutta

We consider the scalar autonomous initial value problem as solved by an explicit Runge-Kutta pair of orders 6 and 5. We focus on an efficient family of such pairs, which were studied extensively in previous decades. This family comes with 5 coefficients that one is able to select arbitrarily. We set, as a fitness function, a certain measure, which is evaluated after running the pair in a couple of relevant problems. Thus, we may adjust the coefficients of the pair, minimizing this fitness function using the differential evolution technique. We conclude with a method (i.e. a Runge-Kutta pair) which outperforms other pairs of the same two orders in a variety of scalar autonomous problems.

Sign in / Sign up

Export Citation Format

Share Document