Estimation of generalized fractional integral operators with nonsingular function as a kernel
AIMS Mathematics, 2021 Bessel function has a significant role in fractional calculus having immense applications in physical and theoretical approach. Present work aims to introduce fractional integral operators in which generalized multi-index Bessel function as a kernel, and
Iqra Nayab +6 more
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Ćirić-type generalized F-contractions with integral inclusion in super metric spaces
Results in Control and OptimizationThis study aims to explore Ćirić-type generalized F-contractions, almost F-contractions, and the combination of these contractions in the framework of super metric spaces.
Kamaleldin Abodayeh +4 more
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Fractal and Fractional, 2021 Considering the large number of fractional operators that exist, and since it does not seem that their number will stop increasing soon at the time of writing this paper, it is presented for the first time, as far as the authors know, a simple and ...
A. Torres-Hernandez, F. Brambila-Paz
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Analysis on nonlinear differential equation with a deviating argument via Faedo–Galerkin method
Results in Applied MathematicsThis article focuses on the impulsive fractional differential equation (FDE) of Sobolev type with a nonlocal condition. Existence and uniqueness of the approximations are determined via analytic semigroup and fixed point method.
M. Manjula +3 more
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Fractional Calculus and Shannon Wavelet [PDF]
Mathematical Problems in Engineering, 2012 An explicit analytical formula for the any order fractional derivative of Shannon wavelet is given as wavelet series based on connection coefficients. So that for any L2(ℝ) function, reconstructed by Shannon wavelets, we can easily define its fractional derivative.
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Fractional order calculus: historical apologia, basic concepts and some applications
Revista Brasileira de Ensino de FísicaFractional order calculus (FOC) deals with integrals and derivatives of arbitrary (i.e., non-integer) order, and shares its origins with classical integral and differential calculus.
S.A. David +2 more
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Fractional Derivatives and the Fundamental Theorem of Fractional Calculus [PDF]
Fractional Calculus and Applied Analysis, 2020 In this paper, we address the one-parameter families of the fractional integrals and derivatives defined on a finite interval. First we remind the reader of the known fact that under some reasonable conditions, there exists precisely one unique family of the fractional integrals, namely, the well-known Riemann-Liouville fractional integrals.
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From Fractional Quantum Mechanics to Quantum Cosmology: An Overture
Mathematics, 2020 Fractional calculus is a couple of centuries old, but its development has been less embraced and it was only within the last century that a program of applications for physics started. Regarding quantum physics, it has been only in the previous decade or
Paulo Vargas Moniz, Shahram Jalalzadeh
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AIMS MathematicsThe aim of this paper was to provide systematic approaches to study the existence of results for the system fractional relaxation integro-differential equations.
Saowaluck Chasreechai +6 more
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Applications of Homogenous Balance Principles Combined with Fractional Calculus Approach and Separate Variable Method on Investigating Exact Solutions to Multidimensional Fractional Nonlinear PDEs [PDF]
, 2020 Ruichao Ren, Shunli Zhang, Weiguo Rui
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