In this article, we develop a mathematical model considering susceptible, exposed, infected, asymptotic, quarantine/isolation and recovered classes as in case of COVID-19 disease. The facility of ...quarantine/isolation have been provided to both exposed and infected classes. Asymptotic individuals either recovered without undergo treatment or moved to infected class after some duration. We have formulated the reproduction number for the proposed model. Elasticity and sensitivity analysis indicates that model is more sensitive towards the transmission rate from exposed to infected classes rather than transmission rate from susceptible to exposed class. Analysis of global stability for the proposed model is studied through Lyapunov’s function.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
The purpose of this paper is to compute two unified fractional integrals involving the product of two H-functions, a general class of polynomials and Appell function
. These integrals are further ...applied in proving two theorems on Saigo-Maeda fractional integral operators. Some consequent results and special cases are also pointed out in the concluding section.
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BFBNIB, DOBA, GIS, IJS, IZUM, KILJ, KISLJ, NUK, PILJ, PNG, SAZU, UILJ, UKNU, UL, UM, UPUK
In this paper, we discuss the phenomenon of miscible flow with longitudinal dispersion in porous media. This process simultaneously occur because of molecular diffusion and convection. Here, we ...analyze the governing differential equation involving Caputo-Fabrizio fractional derivative operator having non singular kernel. Fixed point theorem has been used to prove the uniqueness and existence of the solution of governing differential equation. We apply Laplace transform and use technique of iterative method to obtain the solution. Few applications of the main result are discussed by taking different initial conditions to observe the effect on derivatives of different fractional order on the concentration of miscible fluids.
The paper's main aim is to investigate the 2019 coronavirus disease in Ethiopia using a fractional-order mathematical model. It would also focus on the importance of fractional-order derivatives that ...may help us in modelling the system and understanding the effect of model parameters and fractional derivative orders on the approximate solutions of our model. A SELAIQHCR model is constructed using nonlinear differential equations in the Atangana–Baleanu non-integer operator in the Caputo sense. After that, the Chebyshev fourth kind spectral collocation method is used to change a fractional system to an algebraic system. Newton iterative technique is used to solve the converted system. The next-generation matrix technique is used to obtain the effective reproduction number. The COVID-19-free equilibrium point and endemic equilibrium point, solution positivity and boundedness, and their stability are all carefully done. The sensitivity of the effective reproduction value with respect to the key model parameters is discussed. The beginning values provided for our system were obtained using reports from the Ethiopian Public Health Institute from 29 February 2021 to 7 June 2021. The fundamental reproduction number is obtained with . The model's numerical solutions are represented graphically.
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DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, UILJ, UKNU, UL, UM, UPUK
The study discussed in this article is driven by the realization that many physical processes may be understood by using applications of fractional operators and special functions. In this study, we ...present and examine a fractional integral operator with an I-function in its kernel. This operator is used to solve several fractional differential equations (FDEs). FDE has a set of particular cases whose solutions represent different physical phenomena. Many mathematical physics, biology, engineering, and chemistry problems are identified and solved using FDE. Specifically, a few exciting relations involving the new fractional operator with incomplete I-function (IIF) in its kernel and classical Riemann Liouville fractional integral and derivative operators, the Hilfer fractional derivative operator, and the generalized composite fractional derivate (GCFD) operator are established. The discovery and investigation of several important exceptional cases follow this.
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DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, UILJ, UKNU, UL, UM, UPUK
In this study, we present and examine a fractional integral operator with an
I$$ I $$‐function in its kernel. This operator is used to solve several fractional differential equations (FDEs). FDE has ...a set of particular cases whose solutions represent different physical phenomena. Much mathematical physics, biology, engineering, and chemistry problems are identified and solved using FDE. We first solve the FDE and the integral operator for the incomplete
I$$ I $$‐function (I
I$$ I $$F) for the generalized composite fractional derivative (GCFD). This is followed by the discovery and investigation of several important exceptional cases. The significant finding of this study is a first‐order integer‐differential equation of the Volterra type that clearly describes the unsaturated nature of free‐electron lasers.
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FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SBCE, SBMB, UL, UM, UPUK
This article aims to establish certain image formulas associated with the fractional calculus operators with Appell function in the kernel and Caputo-type fractional differential operators involving ...Srivastava polynomials and extended Mittag-Leffler function. The main outcomes are presented in terms of the extended Wright function. In addition, along with the noted outcomes, the implications are also highlighted.
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IZUM, KILJ, NUK, PILJ, PNG, SAZU, UL, UM, UPUK
By making use of the fractional hypergeometric operators, we establish certain new fractional integral inequalities for synchronous functions which are related to the weighted version of the ...Chebyshev functional. Some consequent results and special cases of the main results are also pointed out.
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FZAB, GIS, IJS, IZUM, KILJ, NLZOH, NUK, OILJ, PILJ, PNG, SAZU, SBCE, SBMB, UL, UM, UPUK
Our aim is to study and investigate the family of
(
p
,
q
)
-extended (
incomplete and complete
) elliptic-type integrals for which the usual properties and representations of various known results ...of the (
classical
) elliptic integrals are extended in a simple manner. This family of elliptic-type integrals involves a number of special cases and has a connection with
(
p
,
q
)
-extended Gauss’ hypergeometric function and
(
p
,
q
)
-extended Appell’s double hypergeometric function
F
1
. Turán-type inequalities including log-convexity properties are proved for these
(
p
,
q
)
-extended complete elliptic-type integrals. Further, we establish various Mellin transform formulas and obtain certain infinite series representations containing Laguerre polynomials. We also obtain some relationship between these
(
p
,
q
)
-extended elliptic-type integrals and Meijer
G
-function of two variables. Moreover, we obtain several connections with
(
p
,
q
)
-extended beta function as special values and deduce numerous differential and integral formulas. In conclusion, we introduce
(
p
,
q
)
-extension of the Epstein–Hubbell (E-H) elliptic-type integral.
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IZUM, KILJ, NUK, PILJ, PNG, SAZU, UL, UM, UPUK
The Bernoulli equation is useful to assess the motility and recovery rate with respect to time in order to measure the COVID-19 outbreak. The homotopy perturbation method was applied in the current ...article to compute the Bernoulli equation. For the existence and uniqueness of solutions, we also used the Caputo–Fabrizio Integral and differential operators. Additionally, we conducted a corresponding investigation for derivatives of integer and fractional orders on the estimated motility and recovery rate.
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DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, UILJ, UKNU, UL, UM, UPUK
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