Results 31 to 40 of about 34,631 (216)

Fractional Differential Equations with the General Fractional Derivatives of Arbitrary Order in the Riemann–Liouville Sense

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
doaj   +1 more source

Comparison principles for fractional differential equations with the Caputo derivatives

Advances in Difference Equations, 2018
In this paper, we deal with comparison principles for fractional differential equations involving the Caputo derivatives of order p with 0≤n ...
Ziqiang Lu, Yuanguo Zhu
doaj   +1 more source

On an Analogy of Fermat’s Theorem for the First-Level General Fractional Derivative and Its Applications

Fractal and Fractional
Fermat’s theorem, often referred to as the interior extrema theorem, is one of the fundamental results in calculus and optimization theory. Recently, the statement of this theorem has been generalized to the case of fractional derivatives.
Mohammed Al-Refai, Yuri Luchko
doaj   +1 more source

Retrospective Analysis of Donor Lymphocyte Infusions in Pediatric Patients With Mixed Chimerism After Hematopoietic Stem Cell Transplantation

Pediatric Blood &Cancer, EarlyView.
ABSTRACT Background Allogeneic hematopoietic stem cell transplantation (alloHSCT) is an essential therapy for several malignant and nonmalignant diseases, but relapse and graft loss remain the principal threats to its success. Routine monitoring of chimerism and minimal residual disease (MRD) enables early detection of imminent recurrence and guides ...
Carmen Junk, Sebastian Michaelis, Michaela Döring, Thomas Eichholz, Ursula Holzer, Martin Ebinger, Tim Flaadt, Rupert Handgretinger, Peter Lang, Jan Frederic Weller, Markus Mezger   +10 more
wiley   +1 more source

A New Mixed Fractional Derivative with Applications in Computational Biology

Computation
This study develops a new definition of a fractional derivative that mixes the definitions of fractional derivatives with singular and non-singular kernels.
Khalid Hattaf
doaj   +1 more source

Lyapunov-type inequalities for fractional differential equations: a survey [PDF]

Surveys in Mathematics and its Applications, 2021
A survey of results on Lyapunov-type inequalities for fractional differential equations associated with a variety of boundary conditions is presented.
Sotiris K. Ntouyas, Bashir Ahmad
doaj  

Venetoclax‐Based Therapy as a Bridge to Hematopoietic Stem Cell Transplantation in Relapsed or Refractory Pediatric Acute Leukemia

Pediatric Blood &Cancer, EarlyView.
ABSTRACT Relapsed and/or refractory (R/R) pediatric acute leukemia carries a dismal prognosis, largely driven by chemoresistance to conventional salvage therapy. The BH3‐mimetic venetoclax, combined with chemotherapy or hypomethylating agents, has demonstrated efficacy in small clinical trials.
Katherine S. Colman, Deborah Meyran, Vajiranee Malalasekera, Heather Weerdenburg, Janine Campbell, Rachel Conyers, Stacie Wang, Hannah Walker, Seong Lin Khaw, Diane Hanna   +9 more
wiley   +1 more source

Gut microbiome and aging—A dynamic interplay of microbes, metabolites, and the immune system

FEBS Letters, EarlyView.
Age‐dependent shifts in microbial communities engender shifts in microbial metabolite profiles. These in turn drive shifts in barrier surface permeability of the gut and brain and induce immune activation. When paired with preexisting age‐related chronic inflammation this increases the risk of neuroinflammation and neurodegenerative diseases.
Aaron Mehl, Eran Blacher
wiley   +1 more source

Wirtinger-type inequalities for Caputo fractional derivatives via Taylor’s formula

Journal of Inequalities and Applications
In this study, we firstly derive a Wirtinger-type result, which gives the connection in between the integral of square of a function and the integral of square of its Caputo fractional derivatives with the help of left-sided and right-sided fractional ...
Samet Erden, Mehmet Zeki Sarıkaya, Burçin Gokkurt Ozdemir, Neslihan Uyanık   +3 more
doaj   +1 more source

On Fractional and Fractal Derivatives in Relation to the Physics of Fractals

Recoletos Multidisciplinary Research Journal, 2013
Fractional and fractal derivatives are both generalizations of the usual derivatives that consider derivatives of non-integer orders. Interest in these generalizations has been triggered by a resurgence of clamor to develop a mathematical tool to ...
Roberto N. Padua, Miraluna L. Herrera, Adriano V. Patac Jr., Michael V. Sabugaa, Gibson T. Maglasang, Mark S. Borres, Jay M. Ontolan   +6 more
doaj   +1 more source