When do fractional differential equations have solutions bounded by the Mittag-Leffler function?
When do fractional differential equations have solutions bounded by the Mittag Leffler function? New research into this question! http://www.degruyter.com/view/j/fca.2015.18.issue-3/fca-2015-0039/fca-2015-0039.xml?format=INT Fract. Calc. Appl. Anal. 18, no. 3 (2015), 642-650. DOI: 10.15
From playlist Mathematical analysis and applications
The Cotangent's Series Expansion Derivation using FOURIER SERIES [ Mittag-Leffler Theorem ]
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From playlist Fourier Series
Can you evaluate this limit with a sum? Subscribe to my channel: https://youtube.com/drpeyam Check out my TikTok channel: https://www.tiktok.com/@drpeyam Follow me on Instagram: https://www.instagram.com/peyamstagram/ Follow me on Twitter: https://twitter.com/drpeyam Teespring merch: http
From playlist Integrals
series of n/2^n as a double summation
We will evaluate the infinite series of n/2^n by using the double summation technique. Thanks to Johannes for the solution. Summation by parts approach by Michael Penn: https://youtu.be/mNIsJ0MgdmU Subscribe for more math for fun videos 👉 https://bit.ly/3o2fMNo 💪 Support this channe
From playlist Sum, math for fun
I define one of the most important constants in mathematics, the Euler-Mascheroni constant. It intuitively measures how far off the harmonic series 1 + 1/2 + ... + 1/n is from ln(n). In this video, I show that the constant must exist. It is an open problem to figure out if the constant is
From playlist Series
Sum of Polynomial Coefficients Challenge
Solution on Lemma: https://www.lem.ma/-K (and additional challenges) Tangentially related good read: http://bit.ly/PascalsTri Twitter: https://twitter.com/PavelGrinfeld
From playlist Problems, Paradoxes, and Sophisms
This lecture is part of an online course on rings and modules. We discuss when taking limits of modules preserves exactness. In particular we give the Mittag-Leffler condition that ensures that taking inverse limits of modules preserves exactness. For the other lectures in the course see
From playlist Rings and modules
Banach fixed point theorem & differential equations
A novel application of Banach's fixed point theorem to fractional differential equations of arbitrary order. The idea involves a new metric based on the Mittag-Leffler function. The technique is applied to gain the existence and uniqueness of solutions to initial value problems. http://
From playlist Mathematical analysis and applications
logarithm of a matrix. I calculate ln of a matrix by finding the eigenvalues and eigenvectors of that matrix and by using diagonalization. It's a very powerful tool that allows us to find exponentials, sin, cos, and powers of a matrix and relates to Fibonacci numbers as well. This is a mus
From playlist Eigenvalues
Gronwall's inequality & fractional differential equations
Several general versions of Gronwall's inequality are presented and applied to fractional differential equations of arbitrary order. Applications include: yielding a priori bounds and nonumultiplicity of solutions. This presentation features new mathematical research. http://projecteucli
From playlist Mathematical analysis and applications
Commutative algebra 48: Limits and exactness
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We discuss when the limit of exact sequences is exact. We show this happens whenever the "Mittag-Leffler condition" is satisfi
From playlist Commutative algebra
Deriving EULER's INFINITE SINE PRODUCT using the Mittag-Leffler Pole Expansion of the Cotangent!
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From playlist Integrals
Hermitian and Non-Hermitian Laplacians and Wave Equaions by Andrey shafarevich
Non-Hermitian Physics - PHHQP XVIII DATE: 04 June 2018 to 13 June 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore Non-Hermitian Physics-"Pseudo-Hermitian Hamiltonians in Quantum Physics (PHHQP) XVIII" is the 18th meeting in the series that is being held over the years in Quantum Phys
From playlist Non-Hermitian Physics - PHHQP XVIII
Lennart Carleson - The Abel Prize interview 2006
0:00 Glimpses of the Abel Prize ceremony made for Norwegian television 05:00 Interview proper starts (Norwegian) 07:46 (English) Almost-everywhere convergence of Fourier series for square-integrable (L^2) functions 10:08 Interesting example of need to have conviction about outcome before c
From playlist The Abel Prize Interviews
Distance point and plane the Lagrange way
In this video, I derive the formula for the distance between a point and a plane, but this time using Lagrange multipliers. This not only gives us a neater way of solving the problem, but also gives another illustration of the method of Lagrange multipliers. Enjoy! Note: Check out this vi
From playlist Partial Derivatives
This Result looks WAY TOO GOOD to be True! Transforming transcendental bois!
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From playlist Taylor Series