A boundary value problem for a random-order fractional differential equation
Results in Applied Mathematics, 2022 In this paper, we define a new Riemann–Liouville fractional integral with random order, from this Caputo and Riemann–Liouville fractional derivatives are straightforward obtained, where the fractional order of these operators is a simple random variable.
Omar U. Lopez-Cresencio +3 more
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Approximation properties of the fractional q-integral of Riemann-Liouville integral type Szasz-Mirakyan-Kantorovich operators [PDF]
, 2022 In the present paper, we introduce the fractional q-integral of Riemann-Liouville integral type Szász-Mirakyan-Kantorovich operators. Korovkin-type approximation theorem is given and the order of convergence of these operators are obtained by using ...
Kara, Mustafa
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Integral inequalities via Raina’s fractional integrals operator with respect to a monotone function
Advances in Difference Equations, 2020 We establish certain new fractional integral inequalities involving the Raina function for monotonicity of functions that are used with some traditional and forthright inequalities.
Shu-Bo Chen +5 more
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Fractal and Fractional, 2023 This paper applies two different types of Riemann–Liouville derivatives to solve fractional differential equations of second order. Basically, the properties of the Riemann–Liouville fractional derivative depend mainly on the lower bound of the integral ...
Abdulrahman B. Albidah
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Riemann Liouville integrals of fractional order and extended KP hierarchy [PDF]
Journal of Physics A: Mathematical and General, 2002 An attempt is given to formulate the extensions of the KP hierarchy by introducing fractional order pseudo-differential operators. In the case of the extension with the half-order pseudo-differential operators, a system analogous to the supersymmetric extensions of the KP hierarchy is obtained.
Kamata, Masaru, Nakamula, Atsushi
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Stabilization of a fractional-order chain of integrators: a contraction-based approach [PDF]
, 2013 In this paper, stabilization of a chain of fractional-order integrators is attempted. The stability is proved using contraction analysis.
SPURGEON, S +8 more
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Integral inequalities for some convex functions via generalized fractional integrals
Journal of Inequalities and Applications, 2018 In this paper, we obtain the Hermite–Hadamard type inequalities for s-convex functions and m-convex functions via a generalized fractional integral, known as Katugampola fractional integral, which is the generalization of Riemann–Liouville fractional ...
Naila Mehreen, Matloob Anwar
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Fractional variational problems depending on indefinite integrals [PDF]
, 2012 We obtain necessary optimality conditions for variational problems with a Lagrangian depending on a Caputo fractional derivative, a fractional and an indefinite integral.
Pooseh, Shakoor +8 more
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Fractal and Fractional, 2022 At present many researchers devote themselves to studying the relationship between continuous fractal functions and their fractional integral. But little attention is paid to the relationship between Mellin transform and fractional integral.
Zhibiao Zhou, Wei Xiao, Yongshun Liang
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Riemann-liouville fractional fundamental theorem of calculus and riemann-liouville fractional polya type integral inequality and its extension to choquet integral setting [PDF]
, 2019 Here we present the right and left Riemann-Liouville fractional fundamental theorems of fractional calculus without any initial conditions for the first time.
Anastassiou, George A.
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