Certain Inequalities Pertaining to Some New Generalized Fractional Integral Operators
Fractal and Fractional, 2021 In this paper, we introduce the generalized left-side and right-side fractional integral operators with a certain modified ML kernel. We investigate the Chebyshev inequality via this general family of fractional integral operators.
Hari Mohan Srivastava +3 more
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New applications of the new general integral transform method with different fractional derivatives
Alexandria Engineering Journal, 2023 Integral transforms are a versatile mathematical technique that can be applied in a wide range of science and engineering fields. We consider the general integral transform with the Caputo derivative and Constant Proportional Caputo derivative in this ...
Ali Akgül +4 more
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A new general integral transform for solving integral equations
Journal of Advanced Research, 2021 Introduction: Integral transforms are important to solve real problems. Appropriate choice of integral transforms helps to convert differential equations as well as integral equations into terms of an algebraic equation that can be solved easily.During ...
Hossein Jafari
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New approach to a generalized fractional integral [PDF]
Applied Mathematics and Computation, 2011 The paper presents a new formula for the fractional integration, which generalizes the Riemann-Liouville and Hadamard fractional integrals into a single form, which when a parameter fixed at different values, produces the above integrals as special cases.
Udita N Katugampola
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The General Fractional Derivative and Related Fractional Differential Equations
Mathematics, 2020 In this survey paper, we start with a discussion of the general fractional derivative (GFD) introduced by A. Kochubei in his recent publications. In particular, a connection of this derivative to the corresponding fractional integral and the Sonine ...
Yuri Luchko, Masahiro Yamamoto
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Haar wavelet fractional derivative [PDF]
Proceedings of the Estonian Academy of Sciences, 2022 In this paper, the fundamental properties of fractional calculus are discussed with the aim of extending the definition of fractional operators by using wavelets.
Carlo Cattani
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New general Grüss-type inequalities over σ-finite measure space with applications
Advances in Difference Equations, 2020 In this paper, we establish some new integral inequalities involving general kernels. We obtain the related broad range of fractional integral inequalities.
Sajid Iqbal +5 more
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Nonlinear generalized fractional differential equations with generalized fractional integral conditions [PDF]
Journal of Taibah University for Science, 2020 This research work is dedicated to an investigation of the existence and uniqueness of a class of nonlinear ψ-Caputo fractional differential equation on a finite interval $[0, T] $, equipped with nonlinear ψ-Riemann–Liouville fractional integral boundary conditions of different orders $0 \lt \alpha , \beta \lt 1 $, we deal with a recently introduced ψ ...
Samiha Belmor +2 more
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Generalized proportional fractional integral functional bounds in Minkowski’s inequalities
Advances in Difference Equations, 2021 In this research paper, we improve some fractional integral inequalities of Minkowski-type. Precisely, we use a proportional fractional integral operator with respect to another strictly increasing continuous function ψ.
Tariq A. Aljaaidi +4 more
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Fractional integral inequalities involving Marichev–Saigo–Maeda fractional integral operator
Journal of Inequalities and Applications, 2020 The aim of this present investigation is establishing Minkowski fractional integral inequalities and certain other fractional integral inequalities by employing the Marichev–Saigo–Maeda (MSM) fractional integral operator.
Asifa Tassaddiq +5 more
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