Some generalized Riemann-Liouville k-fractional integral inequalities [PDF]
Journal of Inequalities and Applications, 2016 The focus of the present study is to prove some new Pólya-Szegö type integral inequalities involving the generalized Riemann-Liouville k-fractional integral operator.
Praveen Agarwal +2 more
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Well-posedness of the initial-boundary value problems for the time-fractional degenerate diffusion equations [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2022 This paper deals with the solving of initial-boundary value problems for the one-dimensional linear timefractional diffusion equations with time-degenerate diffusive coefficients tβ with β>1-α.
A.G. Smadiyeva
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Numerical Approximations and Fractional Calculus: Extending Boole’s Rule with Riemann–Liouville Fractional Integral Inequalities [PDF]
, 2016 This paper develops integral inequalities for first-order differentiable convex functions within the framework of fractional calculus, extending Boole-type inequalities to this domain. An integral equality involving Riemann–Liouville fractional integrals
Hüseyin Budak +9 more
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Evaluating an Improper Fractional Integral Based on Jumarie's Modified Riemann-Liouville Fractional Calculus [PDF]
, 2023 : In this paper, based on Jumarie’s modified Riemann-Liouville (R-L) fractional calculus, we find the solution of some type of improper fractional integral.
Chii-Huei Yu
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A Comprehensive Review on the Fejér-Type Inequality Pertaining to Fractional Integral Operators
Axioms, 2023 A review of the results on the fractional Fejér-type inequalities, associated with different families of convexities and different kinds of fractional integrals, is presented.
Muhammad Tariq +2 more
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Maclaurin-type inequalities for Riemann-Liouville fractional integrals
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica, 2023 The authors give estimates for the modulus of the difference \[ D(f,a,b,\alpha):=\frac{1}{8}\big[3f((5a+b)/6)+2f((a+b)/2)+2f((a+3b)/6)\big]-\frac{\Gamma(\alpha+1)}{2(b-a)^\alpha}\big[J_{a+}^{\alpha} f(b)+J_{b-}^{\alpha} f(a)\big] \] where \(f\in L_1[a,b]\) and \[ J_{a+}^{\alpha}f(x):=\frac{1}{\Gamma(\alpha)}\int_a^x (x-t)^{\alpha-1}f(t)dt,\,\,x>a \] \[
Hezenci, Fatih, BUDAK, HÜSEYİN
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Riemann–Liouville fractional integral of non-affine fractal interpolation function and its fractional operator [PDF]
, 2021 This paper mainly investigates the Riemann–Liouville fractional integral of $$\alpha $$-fractal function and fractional operator of $$\alpha $$-fractal function that maps the given continuous function to its Riemann–Liouville fractional integral.
T. M. C. Priyanka, A. Gowrisankar
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Some New Riemann-Liouville Fractional Integral Inequalities [PDF]
International Journal of Mathematics and Mathematical Sciences, 2014 In this paper, some new fractional integral inequalities are established.
Jessada Tariboon +2 more
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Numerical Approximations of the Riemann–Liouville and Riesz Fractional Integrals
Informatica, 2023 In this paper, the numerical algorithms for calculating the values of the left- and right-sided Riemann–Liouville fractional integrals and the Riesz fractional integral using spline interpolation techniques are derived. The linear, quadratic and three variants of cubic splines are taken into account.
Mariusz Ciesielski, Grzegorz Grodzki
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Integral Inequalities for s-Convexity via Generalized Fractional Integrals on Fractal Sets
Mathematics, 2020 In this study, we establish new integral inequalities of the Hermite−Hadamard type for s-convexity via the Katugampola fractional integral. This generalizes the Hadamard fractional integrals and Riemann−Liouville into a single form.
Ohud Almutairi, Adem Kılıçman
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