Bilinear Fractional Integral Along Homogeneous Curves
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DOI: 10.1007/s00041-016-9511-9
Abstract: The boundedness of the bilinear fractional integrals along homogeneous curves $$\gamma (t)=(t^{\alpha _1},t^{\alpha _2})$$γ(t)=(tα1,tα2) with $$\alpha _2>\alpha _1\ge 1$$α2>α1≥1 is obtained. The authors extend the results of the bilinear fractional integrals of Kenig and Stein… read more here.
Keywords: alpha alpha; homogeneous curves; bilinear fractional; integral along ... See more keywords
Fractional integral sliding modes for robust tracking of nonlinear systems
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DOI: 10.1007/s11071-016-3086-5
Abstract: Memory and heritage of differintegral operators require knowledge of the error manifold derivative at the initial time to sustain a sliding motion for any initial condition. Moreover, when the system is subject to (unknown) disturbances,… read more here.
Keywords: sliding mode; sliding modes; integral sliding; fractional integral ... See more keywords
New Fractional Integral Inequalities for Differentiable Convex Functions and Their Applications
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DOI: 10.1007/s11253-017-1376-9
Abstract: We establish some new fractional integral inequalities for differentiable convex functions and give several applications for the Beta-function. read more here.
Keywords: new fractional; convex functions; integral inequalities; inequalities differentiable ... See more keywords
On the $$\Psi $$Ψ-fractional integral and applications
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DOI: 10.1007/s40314-019-0774-z
Abstract: Motivated by the $$\Psi $$Ψ-Riemann–Liouville $$(\Psi -\mathrm{RL})$$(Ψ-RL) fractional derivative and by the $$\Psi $$Ψ-Hilfer $$(\Psi -\mathrm{H})$$(Ψ-H) fractional derivative, we introduced a new fractional operator the so-called $$\Psi $$Ψ-fractional integral. We present some important results by… read more here.
Keywords: psi; psi fractional; fractional integral; integral applications ... See more keywords
Interrelationships Between Marichev–Saigo–Maeda Fractional Integral Operators, the Laplace Transform and the $${\overline{H}}$$H¯-Function
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DOI: 10.1007/s40819-019-0690-3
Abstract: AbstractIn this article, we first evaluate the Laplace transform of Marichev–Saigo–Maeda (M–S–M) fractional integral operators whose kernel is the Appell function $$F_{3}$$F3 and point out its six special cases (Saigo, Erdélyi–Kober, Riemann–Liouville and Weyl fractional… read more here.
Keywords: laplace transform; marichev saigo; saigo maeda; integral operators ... See more keywords
Certain Bounds Related to Multi-Parameterized $k$ -Fractional Integral Inequalities and Their Applications
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DOI: 10.1109/access.2019.2938341
Abstract: A $k$ -fractional integral identity with multiple parameters is investigated. Based on this identity, some estimation-type results related to $k$ -fractional integral inequalities for the first-order differentiable functions are obtained. These results are then applied… read more here.
Keywords: integral inequalities; tex math; inline formula; fractional integral ... See more keywords
A Fractional Integral and Fractal Dimension-Based Deep Learning Approach for Pavement Crack Detection in Transportation Service Management
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DOI: 10.1109/tnsm.2022.3197457
Abstract: With artificial intelligence prevailing in intelligent transportation system, pavement crack detection with deep learning has aroused wide attentions in both academia and transportation sector. Nevertheless, it still remains a challenge to accomplish crack detection due… read more here.
Keywords: fractional integral; fractal dimension; crack detection; transportation ... See more keywords
SOME REMARKS ON FRACTIONAL INTEGRAL OF ONE-DIMENSIONAL CONTINUOUS FUNCTIONS
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DOI: 10.1142/s0218348x2050005x
Abstract: In this paper, we make research on Katugampola and Hadamard fractional integral of one-dimensional continuous functions on [0, 1]. We proved that Katugampola fractional integral of bounded and cont... read more here.
Keywords: dimensional continuous; continuous functions; integral one; remarks fractional ... See more keywords
THE STRUCTURAL FEATURES OF HILBERT-TYPE LOCAL FRACTIONAL INTEGRAL INEQUALITIES WITH ABSTRACT HOMOGENEOUS KERNEL AND ITS APPLICATIONS
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DOI: 10.1142/s0218348x2050111x
Abstract: In this paper, by using the theory of local fractional calculus and some techniques of real analysis, the structural characteristics of Hilbert-type local fractional integral inequalities with abstract homogeneous kernel are studied. At the same… read more here.
Keywords: inequalities abstract; local fractional; hilbert type; integral inequalities ... See more keywords
Fractional Integral and Derivative Formulas by Using Marichev-Saigo-Maeda Operators Involving the S-Function
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DOI: 10.1155/2019/6487687
Abstract: We establish fractional integral and derivative formulas by using Marichev-Saigo-Maeda operators involving the S-function. The results are expressed in terms of the generalized Gauss hypergeometric functions. Corresponding assertions in terms of Saigo, Erdélyi-Kober, Riemann-Liouville, and… read more here.
Keywords: using marichev; marichev saigo; derivative formulas; integral derivative ... See more keywords
Some Inequalities of Generalized p-Convex Functions concerning Raina’s Fractional Integral Operators
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DOI: 10.1155/2021/3089553
Abstract: Convex functions play an important role in pure and applied mathematics specially in optimization theory. In this paper, we will deal with well-known class of convex functions named as generalized p-convex functions. We develop Hermite–Hadamard-type… read more here.
Keywords: raina fractional; mathematics; convex functions; generalized convex ... See more keywords