• 호남수학학술지
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• 제45권2호
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• pp.340-358
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• 2023

This article establishes an equality for the case of twice-differentiable convex functions with respect to the conformable fractional integrals. With the help of this identity, we prove sundry midpoint-type inequalities by twice-differentiable convex functions according to conformable fractional integrals. Several important inequalities are obtained by taking advantage of the convexity, the Hölder inequality, and the power mean inequality. Using the specific selection of our results, we obtain several new and well-known results in the literature.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제25권3호
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• pp.132-148
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• 2021

The modified F-expansion method is used to construct analytical solutions of the foam drainage equation with time- and space-fractional derivatives. The conformable derivatives are considered as spacial and temporal ones. As a result, some analytical exact solutions including kink, bright-dark soliton, periodic and rational solutions are obtained.

• Kyungpook Mathematical Journal
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• 제61권1호
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• pp.139-153
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• 2021

In this paper, we study the existence of positive solutions for a class of conformable fractional differential equations with integral boundary conditions. By using the properties of Green's function with the fixed point theorem in a cone, we prove the existence of a positive solution. We also provide some examples to illustrate our results.

• Nonlinear Functional Analysis and Applications
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• 제29권2호
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• pp.597-620
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• 2024

In this study, the conformable fractional derivative(CFD) of order 𝝔 in conjunction with the LC operator of orderρ is used to develop the model of the transmission of the A(H1N1) influenza infection. A brand-new A(H1N1) influenza infection model is presented, with a population split into four different compartments. Fixed point theorems were used to prove the existence of the solutions and uniqueness of this model. The basic reproduction number R₀ was determined. The least and most sensitive variables that could alter R₀ were then determined using normalized forward sensitivity indices. Through numerical simulations carried out with the aid of the Adams-Moulton approach, the study also investigated the effects of numerous biological characteristics on the system. The findings demonstrated that if 𝝔 < 1 and ρ < 1 under the CFD, also the findings demonstrated that if 𝝔 = 1 and ρ = 1 under the CFD, the A(H1N1) influenza infection will not vanish.

• 대한수학회논문집
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• 제37권2호
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• pp.503-520
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• 2022

We introduce a new type of fractional derivative, which we call as the right local general truncated M-fractional derivative for α-differentiable functions that generalizes the fractional derivative type introduced by Anastassiou. This newly defined operator generalizes the standard properties and results of the integer order calculus viz. the Rolle's theorem, the mean value theorem and its extension, inverse property, the fundamental theorem of calculus and the theorem of integration by parts. Then we represent a relation of the newly defined fractional derivative with known fractional derivative and in context with this derivative a physical problem, Kirchoff's voltage law, is generalized. Also, the importance of this newly defined operator with respect to the flexibility in the parametric values is described via the comparison of the solutions in the graphs using MATLAB software.