Investigating a Class of Generalized Caputo-Type Fractional Integro-Differential Equations

Ali, Saeed M.; Shatanawi, Wasfı; Kassim, Mohammed D.; Abdo, Mohammed S.; Saleh, S.

doi:10.1155/2022/8103046

Cited by 4 publications

(1 citation statement)

References 24 publications

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“…This result was generalized to differential equations, and it was believed that Obloza was the first to make this generalization [28], after which Alsina and Ger published a scientific paper containing what is known today as the Hyers-Ulam stability [29], Rus investigated the Hyers-Ulam stability of differential and integral equations using the Gronwall lemma [30]. Recently, the Hyers-Ulam stability problems of several differential equations were investigated by using the method of integral operators, see [31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Modeling Drug Concentration in Blood through Caputo-Fabrizio and Caputo Fractional Derivatives

Awadalla¹,

Abuasbeh²,

Noupoue³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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This study focuses on the dynamics of drug concentration in the blood. In general, the concentration level of a drug in the blood is evaluated by the mean of an ordinary and first-order differential equation. More precisely, it is solved through an initial value problem. We proposed a new modeling technique for studying drug concentration in blood dynamics. This technique is based on two fractional derivatives, namely, Caputo and Caputo-Fabrizio derivatives. We first provided comprehensive and detailed proof of the existence of at least one solution to the problem; we later proved the uniqueness of the existing solution. The proof was written using the Caputo-Fabrizio fractional derivative and some fixed-point techniques. Stability via the Ulam-Hyers (UH) technique was also investigated. The application of the proposed model on two real data sets revealed that the Caputo derivative was more suitable in this study. Indeed, for the first data set, the model based on the Caputo derivative yielded a Mean Squared Error (MSE) of 0.03095 with a corresponding best value of fractional order of derivative of 1.00360. Caputo-Fabrizio-basedderivative appeared to be the second-best method for the problem, with an MSE of 0.04324 for a corresponding best fractional derivative order of 0.43532. For the second experiment, Caputo derivative-based model still performed the best as it yielded an MSE of 0.04066, whereas the classical and the Caputo-Fabrizio methods were tied with the same MSE of 0.07299. Another interesting finding was that the MSE yielded by the Caputo-Fabrizio fractional derivative coincided with the MSE obtained from the classical approach.

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Section: Introductionmentioning

confidence: 99%

Modeling Drug Concentration in Blood through Caputo-Fabrizio and Caputo Fractional Derivatives

Awadalla¹,

Abuasbeh²,

Noupoue³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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On solutions of a hybrid generalized Caputo-type problem via the noncompactness measure in the generalized version of Darbo’s criterion

et al. 2023

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In this manuscript, we study the existence and uniqueness of solutions for a new neutral hybrid nonlinear differential equation in the context of a fractional generalized operator in the sense of ψ-Caputo. To emphasize the novelty of the manuscript, a pure technique of the noncompactness measures is applied to a hybrid system based on the notion of the modulus of continuity in Darbo’s criterion that covers the existing results of other works published before. The Ulam–Hyers and generalized Ulam–Hyers stabilities are explored for the given neutral nonhybrid nonlinear problem. An application is prepared in the framework of an example to ensure the validity of theorems for different cases.

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Analytic technique for solving temporal time-fractional gas dynamics equations with Caputo fractional derivative

Alaroud

Ababneh

Tahat

et al. 2022

MATH

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<abstract><p>Constructing mathematical models of fractional order for real-world problems and developing numeric-analytic solutions are extremely significant subjects in diverse fields of physics, applied mathematics and engineering problems. In this work, a novel analytical treatment technique called the Laplace residual power series (LRPS) technique is performed to produce approximate solutions for a non-linear time-fractional gas dynamics equation (FGDE) in a multiple fractional power series (MFPS) formula. The LRPS technique is a coupling of the RPS approach with the Laplace transform operator. The implementation of the proposed technique to handle time-FGDE models is introduced in detail. The MFPS solution for the target model is produced by solving it in the Laplace space by utilizing the limit concept with fewer computations and more accuracy. The applicability and performance of the technique have been validated via testing three attractive initial value problems for non-linear FGDEs. The impact of the fractional order <italic>β</italic> on the behavior of the MFPS approximate solutions is numerically and graphically described. The <italic>j</italic>th MFPS approximate solutions were found to be in full harmony with the exact solutions. The solutions obtained by the LRPS technique indicate and emphasize that the technique is easy to perform with computational efficiency for different kinds of time-fractional models in physical phenomena.</p></abstract>

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Investigating a Class of Generalized Caputo-Type Fractional Integro-Differential Equations

Cited by 4 publications

References 24 publications

Modeling Drug Concentration in Blood through Caputo-Fabrizio and Caputo Fractional Derivatives

Modeling Drug Concentration in Blood through Caputo-Fabrizio and Caputo Fractional Derivatives

On solutions of a hybrid generalized Caputo-type problem via the noncompactness measure in the generalized version of Darbo’s criterion

Analytic technique for solving temporal time-fractional gas dynamics equations with Caputo fractional derivative

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