Results 51 to 60 of about 2,390 (148)
International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.In this work, we study the existence and uniqueness of mild solutions for linear and semilinear control systems using the new deformable fractional derivative. The results have been obtained and presented using the deformable Laplace transform and its inverse, as well as the theory of semigroups and a rigorous application of Banach’s fixed‐point ...
Boulkhairy Sy +3 more
wiley +1 more source
Extended Riemann-Liouville type fractional derivative operator with applications
Open Mathematics, 2017 The main purpose of this paper is to introduce a class of new extended forms of the beta function, Gauss hypergeometric function and Appell-Lauricella hypergeometric functions by means of the modified Bessel function of the third kind.
Agarwal P., Nieto Juan J., Luo M.-J.
doaj +1 more source
Convolution Products in L1(R+), Integral Transforms and Fractional Calculus [PDF]
, 2005 Mathematics Subject Classification: 43A20, 26A33 (main), 44A10, 44A15We prove equalities in the Banach algebra L1(R+). We apply them to integral transforms and fractional calculus.* Partially supported by Project BFM2001-1793 of the MCYT-DGI and FEDER ...
Miana, Pedro
core
International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.The Y‐function has emerged as a significant tool in generalized fractional calculus due to its ability to unify and extend numerous classical special functions and hypergeometric‐type functions. Applying the Marichev–Saigo–Maeda fractional integration and differentiation operators of any complex order to the Y‐function, this study establishes four ...
Engdasew Birhane +2 more
wiley +1 more source
Theorem for Series in Three-Parameter Mittag-Leffler Function [PDF]
, 2010 Mathematics Subject Classification 2010: 26A33, 33E12.The new result presented here is a theorem involving series in the three-parameter Mittag-Leffler function. As a by-product, we recover some known results and discuss corollaries.
Camargo, Rubens +3 more
core
Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.In this manuscript, we establish existence, uniqueness, and trajectory controllability for higher order noninstantaneous impulsive fractional neutral stochastic differential equations. First, solvability and uniqueness results are obtained using a fixed‐point approach with appropriate assumptions on nonlinear functions. Next, we deal with the strongest
Dhanalakshmi Kasinathan +5 more
wiley +1 more source
Advances in Difference Equations, 2011 A second-order abstract problem of neutral type with derivatives of non-integer order in the nonlinearity as well as in the nonlocal conditions is investigated. This model covers many of the existing models in the literature. It extends the integer order
Tatar Nasser-eddine
doaj
Demonstratio MathematicaGenerally, fractional partial integro-differential equations (FPIDEs) play a vital role in modeling various complex phenomena. Because of the several applications of FPIDEs in applied sciences, mathematicians have taken a keen interest in developing and ...
Khan Qasim +4 more
doaj +1 more source
Moroccan Journal of Pure and Applied Analysis, 2022 Using generalized Canavati fractional left and right vectorial Taylor formulae we establish mixed fractional Ostrowski, Opial and Grüss type inequalities involving several Banach algebra valued functions. The estimates are with respect to all norms ‖ · ‖
Anastassiou George A.
doaj +1 more source
A Poster about the Old History of Fractional Calculus [PDF]
, 2010 MSC 2010: 26A33, 05C72, 33E12, 34A08, 34K37, 35R11, 60G22The fractional calculus (FC) is an area of intensive research and development. In a previous paper and poster we tried to exhibit its recent state, surveying the period of 1966-2010.
Kiryakova, Virginia +2 more
core