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On the 1st-Level General Fractional Derivatives of Arbitrary Order
Fractal and Fractional, 2023 In this paper, the 1st-level general fractional derivatives of arbitrary order are defined and investigated for the first time. We start with a generalization of the Sonin condition for the kernels of the general fractional integrals and derivatives and ...
Yuri Luchko
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Operational Calculus for the General Fractional Derivatives of Arbitrary Order
Mathematics, 2022 In this paper, we deal with the general fractional integrals and the general fractional derivatives of arbitrary order with the kernels from a class of functions that have an integrable singularity of power function type at the origin.
Maryam Al-Kandari +2 more
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Mathematics, 2022 In this paper, we first consider the general fractional derivatives of arbitrary order defined in the Riemann–Liouville sense. In particular, we deduce an explicit form of their null space and prove the second fundamental theorem of fractional calculus ...
Yuri Luchko
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General Fractional Integrals and Derivatives of Arbitrary Order [PDF]
Symmetry, 2021 In this paper, we introduce the general fractional integrals and derivatives of arbitrary order and study some of their basic properties and particular cases. First, a suitable generalization of the Sonine condition is presented, and some important classes of the kernels that satisfy this condition are introduced.
Yuri Luchko, Luchko Yuri
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Fractal and Fractional, 2022 In this article, a new method for obtaining closed-form solutions of the simplified modified Camassa-Holm (MCH) equation, a nonlinear fractional partial differential equation, is suggested.
Muhammad Shakeel +2 more
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Electrical Circuits RC, LC, and RLC under Generalized Type Non-Local Singular Fractional Operator
Fractal and Fractional, 2021 The current study is of interest when performing a useful extension of a crucial physical problem through a non-local singular fractional operator. We provide solutions that include three arbitrary parameters α, ρ, and γ for the Resistance-Capacitance ...
Bahar Acay, Mustafa Inc
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Advances in Difference Equations, 2020 In the present work, a numerical technique for solving a general form of nonlinear fractional order integro-differential equations (GNFIDEs) with linear functional arguments using Chebyshev series is presented.
Khalid K. Ali +5 more
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Exact radially symmetric solutions to n-dimensional space–time fractional diffusion equations: Resolution of singularities via generalized Hankel transforms [PDF]
AIP AdvancesWe present, for the first time, exact radially symmetric solutions to the n-dimensional space–time fractional diffusion equation with point source initial conditions, employing the most general fractional framework: the Riemann–Liouville temporal ...
Farrukh A. Chishtie
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Response of Fractionally Damped Beams with General Boundary Conditions Subjected to Moving Loads
Shock and Vibration, 2012 This paper presents the transverse vibration of Bernoulli-Euler homogeneous isotropic damped beams with general boundary conditions. The beams are assumed to be subjected to a load moving at a uniform velocity.
R. Abu-Mallouh +3 more
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Nonlocal q-fractional boundary value problem with Stieltjes integral conditions
Nonlinear Analysis, 2019 In this paper, we are dedicated to investigating a new class of one-dimensional lower-order fractional q-differential equations involving integral boundary conditions supplemented with Stieltjes integral.
Jing Ren, Chengbo Zhai
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