Results 31 to 40 of about 12,310,207 (201)
, 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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Fractal and Fractional, 2022 A general system of fractional differential equations with coupled fractional Stieltjes integrals and a Riemann–Liouville fractional integral in boundary conditions is studied in the context of pattern formation.
Yuan Ma, Dehong Ji
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ON GENERAL EULERIAN INTEGRAL FORMULAS AND FRACTIONAL INTEGRATION
Tamkang Journal of Mathematics, 1999 In the present work, we evaluate a unified Eulerian type integral whose integrand involves the product of a polynomial system and the multivariable H-function having general arguments. Our integral formula encompasses a very large number of integrals and provides interesting unifieation and extensions of several known (e.g., [1 ...
Gupta, K. C. +2 more
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Generalized Fractional-Order Discrete-Time Integrator [PDF]
Complexity, 2017 We investigate a generalization of discrete-time integrator. Proposed linear discrete-time integrator is characterised by the variable, fractional order of integration/summation. Graphical illustrations of an analysis of particular vector matrices are presented. In numerical examples, we show relations between the order functions and element responses.
Dorota Mozyrska, Piotr Ostalczyk
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Two Integral Representations for the Relaxation Modulus of the Generalized Fractional Zener Model
Fractal and Fractional, 2023 A class of generalized fractional Zener-type viscoelastic models with general fractional derivatives is considered. Two integral representations are derived for the corresponding relaxation modulus. The first representation is established by applying the
Emilia Bazhlekova, Sergey Pshenichnov
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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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On generalization conformable fractional integral inequalities
Filomat, 2018 The main issues addressed in this paper are making generalization of Gronwall, Volterra and Pachpatte type inequalities for conformable differential equations. By using the Katugampola definition for conformable calculus we found some upper and lower bound for integral inequalities.
Usta, Fuat, Sarıkaya, Mehmet Zeki
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Fractional Integrals and Generalized Olsen Inequalities
Kyungpook mathematical journal, 2009 Summary: Let \(T_\rho\) be the generalized fractional integral operator associated to a function \(\rho:(0,\infty)\to(0,\infty)\), as defined in [\textit{E. Nakai}, Taiwanese J. Math. 5, No.~3, 587--602 (2001; Zbl 0990.26007)]. For a function \(W\) on \(\mathbb R^n\), we be interested in the boundedness of the multiplication operator \(f\mapsto W\cdot ...
Hendra Gunawan, Eridani
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Generalizations of some fractional integral inequalities via generalized Mittag-Leffler function
Journal of Inequalities and Applications, 2017 Fractional inequalities are useful in establishing the uniqueness of solution for partial differential equations of fractional order. Also they provide upper and lower bounds for solutions of fractional boundary value problems.
Ghulam Abbas +3 more
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Fractional integrals of generalized functions [PDF]
Journal of the Australian Mathematical Society, 1972 The concept of integrals of fractional order of a function f, defined by if Reα > 0, can be extended to generalised functions in the framework of the theory of convolution of distributions. The resulting theory [2, Chap. I §5.5] is very satisfactory for many purposes but there are circumstances in which it is not suitable.
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