On tempered fractional calculus with respect to functions and the associated fractional differential equations [PDF]
Mathematical methods in the applied sciences, 2021 The prime aim of the present paper is to continue developing the theory of tempered fractional integrals and derivatives of a function with respect to another function.
Ashwini D. Mali +3 more
semanticscholar +1 more source
General Fractional Vector Calculus
Mathematics, 2021 A generalization of fractional vector calculus (FVC) as a self-consistent mathematical theory is proposed to take into account a general form of non-locality in kernels of fractional vector differential and integral operators.
Vasily E. Tarasov
doaj +1 more source
General Fractional Calculus: Multi-Kernel Approach [PDF]
Mathematics, 2021 For the first time, a general fractional calculus of arbitrary order was proposed by Yuri Luchko in 2021. In Luchko works, the proposed approaches to formulate this calculus are based either on the power of one Sonin kernel or the convolution of one ...
V. Tarasov
semanticscholar +1 more source
Dynamical Behaviour and Chaotic Phenomena of HIV Infection through Fractional Calculus
Discrete Dynamics in Nature and Society, 2022 The infection of human immunodeficiency virus (HIV) is a serious and potentially incurable infection. There is no cure for HIV and is a public health issue around the world.
Rashid Jan +3 more
semanticscholar +1 more source
Enhancing the Mathematical Theory of Nabla Tempered Fractional Calculus: Several Useful Equations
Fractal and Fractional, 2023 Although many applications of fractional calculus have been reported in literature, modeling the physical world using this technique is still a challenge. One of the main difficulties in solving this problem is that the long memory property is necessary,
Yiheng Wei +3 more
doaj +1 more source
An operational calculus formulation of fractional calculus with general analytic kernels
Electronic Research Archive, 2022 Fractional calculus with analytic kernels provides a general setting of integral and derivative operators that can be connected to Riemann–Liouville fractional calculus via convergent infinite series.
Noosheza Rani , Arran Fernandez
doaj +1 more source
On the solutions of some fractional q-differential equations with the Riemann-Liouville fractional q-derivative [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2021 This paper is devoted to explicit and numerical solutions to linear fractional q -difference equations and the Cauchy type problem associated with the Riemann-Liouville fractional q -derivative in q -calculus.
S. Shaimardan, N.S. Tokmagambetov
doaj +2 more sources
Special Functions of Fractional Calculus in the Form of Convolution Series and Their Applications [PDF]
Mathematics, 2021 In this paper, we first discuss the convolution series that are generated by Sonine kernels from a class of functions continuous on a real positive semi-axis that have an integrable singularity of power function type at point zero.
Yuri Luchko
semanticscholar +1 more source
Fractional calculus in the sky
, 2021 Fractional calculus was born in 1695 on September 30 due to a very deep question raised in a letter of L’Hospital to Leibniz. The prophetical answer of Leibniz to that deep question encapsulated a huge inspiration for all generations of scientists and is
D. Baleanu, R. Agarwal
semanticscholar +1 more source
Fractional calculus, zeta functions and Shannon entropy
, 2021 This paper deals with the fractional calculus of zeta functions. In particular, the study is focused on the Hurwitz ζ \zeta function. All the results are based on the complex generalization of the Grünwald-Letnikov fractional derivative.
E. Guariglia
semanticscholar +1 more source