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1 – 8 of 8This study describes the applicability of the a priori estimate method on a nonlocal nonlinear fractional differential equation for which the weak solution's existence and…
Abstract
Purpose
This study describes the applicability of the a priori estimate method on a nonlocal nonlinear fractional differential equation for which the weak solution's existence and uniqueness are proved. The authors divide the proof into two sections for the linear associated problem; the authors derive the a priori bound and demonstrate the operator range density that is generated. The authors solve the nonlinear problem by introducing an iterative process depending on the preceding results.
Design/methodology/approach
The functional analysis method is the a priori estimate method or energy inequality method.
Findings
The results show the efficiency of a priori estimate method in the case of time-fractional order differential equations with nonlocal conditions. Our results also illustrate the existence and uniqueness of the continuous dependence of solutions on fractional order differential equations with nonlocal conditions.
Research limitations/implications
The authors’ work can be considered a contribution to the development of the functional analysis method that is used to prove well-positioned problems with fractional order.
Originality/value
The authors confirm that this work is original and has not been published elsewhere, nor is it currently under consideration for publication elsewhere.
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Arshi Meraj and Dwijendra N. Pandey
This paper is concerned with the existence of mild solutions for a class of fractional semilinear integro-differential equations having non-instantaneous impulses. The result is…
Abstract
This paper is concerned with the existence of mild solutions for a class of fractional semilinear integro-differential equations having non-instantaneous impulses. The result is obtained by using noncompact semigroup theory and fixed point theorem. The obtained result is illustrated by an example at the end.
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M. Iadh Ayari and Sabri T.M. Thabet
This paper aims to study qualitative properties and approximate solutions of a thermostat dynamics system with three-point boundary value conditions involving a nonsingular kernel…
Abstract
Purpose
This paper aims to study qualitative properties and approximate solutions of a thermostat dynamics system with three-point boundary value conditions involving a nonsingular kernel operator which is called Atangana-Baleanu-Caputo (ABC) derivative for the first time. The results of the existence and uniqueness of the solution for such a system are investigated with minimum hypotheses by employing Banach and Schauder's fixed point theorems. Furthermore, Ulam-Hyers
Design/methodology/approach
This paper considered theoretical and numerical methodologies.
Findings
This paper contains the following findings: (1) Thermostat fractional dynamics system is studied under ABC operator. (2) Qualitative properties such as existence, uniqueness and Ulam–Hyers–Rassias stability are established by fixed point theorems and nonlinear analysis topics. (3) Approximate solution of the problem is investigated by Adomain decomposition method. (4) Convergence analysis of ADM is proved. (5) Examples are provided to illustrate theoretical and numerical results. (6) Numerical results are compared with exact solution in tables and figures.
Originality/value
The novelty and contributions of this paper is to use a nonsingular kernel operator for the first time in order to study the qualitative properties and approximate solution of a thermostat dynamics system.
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Gopal Shruthi and Murugan Suvinthra
The purpose of this paper is to study large deviations for the solution processes of a stochastic equation incorporated with the effects of nonlocal condition.
Abstract
Purpose
The purpose of this paper is to study large deviations for the solution processes of a stochastic equation incorporated with the effects of nonlocal condition.
Design/methodology/approach
A weak convergence approach is adopted to establish the Laplace principle, which is same as the large deviation principle in a Polish space. The sufficient condition for any family of solutions to satisfy the Laplace principle formulated by Budhiraja and Dupuis is used in this work.
Findings
Freidlin–Wentzell type large deviation principle holds good for the solution processes of the stochastic functional integral equation with nonlocal condition.
Originality/value
The asymptotic exponential decay rate of the solution processes of the considered equation towards its deterministic counterpart can be estimated using the established results.
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Tarikul Islam and Armina Akter
Fractional order nonlinear evolution equations (FNLEEs) pertaining to conformable fractional derivative are considered to be revealed for well-furnished analytic solutions due to…
Abstract
Purpose
Fractional order nonlinear evolution equations (FNLEEs) pertaining to conformable fractional derivative are considered to be revealed for well-furnished analytic solutions due to their importance in the nature of real world. In this article, the autors suggest a productive technique, called the rational fractional
Design/methodology/approach
The rational fractional
Findings
Achieved fresh and further abundant closed form traveling wave solutions to analyze the inner mechanisms of complex phenomenon in nature world which will bear a significant role in the of research and will be recorded in the literature.
Originality/value
The rational fractional
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Salah Benhiouna, Azzeddine Bellour and Rachida Amiar
A generalization of Ascoli–Arzelá theorem in Banach spaces is established. Schauder's fixed point theorem is used to prove the existence of a solution for a boundary value problem…
Abstract
Purpose
A generalization of Ascoli–Arzelá theorem in Banach spaces is established. Schauder's fixed point theorem is used to prove the existence of a solution for a boundary value problem of higher order. The authors’ results are obtained under, rather, general assumptions.
Design/methodology/approach
First, a generalization of Ascoli–Arzelá theorem in Banach spaces in Cn is established. Second, this new generalization with Schauder's fixed point theorem to prove the existence of a solution for a boundary value problem of higher order is used. Finally, an illustrated example is given.
Findings
There is no funding.
Originality/value
In this work, a new generalization of Ascoli–Arzelá theorem in Banach spaces in Cn is established. To the best of the authors’ knowledge, Ascoli–Arzelá theorem is given only in Banach spaces of continuous functions. In the second part, this new generalization with Schauder's fixed point theorem is used to prove the existence of a solution for a boundary value problem of higher order, where the derivatives appear in the non-linear terms.
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Sabri T.M. Thabet, Bashir Ahmad and Ravi P. Agarwal
In this paper, we study a Cauchy-type problem for Hilfer fractional integrodifferential equations with boundary conditions. The existence of solutions for the given problem is…
Abstract
In this paper, we study a Cauchy-type problem for Hilfer fractional integrodifferential equations with boundary conditions. The existence of solutions for the given problem is proved by applying measure of noncompactness technique in an abstract weighted space. Moreover, we use generalized Gronwall inequality with singularity to establish continuous dependence and uniqueness of
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Paravee Maneejuk, Binxiong Zou and Woraphon Yamaka
The primary objective of this study is to investigate whether the inclusion of convertible bond prices as important inputs into artificial neural networks can lead to improved…
Abstract
Purpose
The primary objective of this study is to investigate whether the inclusion of convertible bond prices as important inputs into artificial neural networks can lead to improved accuracy in predicting Chinese stock prices. This novel approach aims to uncover the latent potential inherent in convertible bond dynamics, ultimately resulting in enhanced precision when forecasting stock prices.
Design/methodology/approach
The authors employed two machine learning models, namely the backpropagation neural network (BPNN) model and the extreme learning machine neural networks (ELMNN) model, on empirical Chinese financial time series data.
Findings
The results showed that the convertible bond price had a strong predictive power for low-market-value stocks but not for high-market-value stocks. The BPNN algorithm performed better than the ELMNN algorithm in predicting stock prices using the convertible bond price as an input indicator for low-market-value stocks. In contrast, ELMNN showed a significant decrease in prediction accuracy when the convertible bond price was added.
Originality/value
This study represents the initial endeavor to integrate convertible bond data into both the BPNN model and the ELMNN model for the purpose of predicting Chinese stock prices.
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