Results 61 to 70 of about 2,452 (143)

A Poster about the Recent History of Fractional Calculus [PDF]

, 2010
MSC 2010: 26A33, 05C72, 33E12, 34A08, 34K37, 35R11, 60G22In the last decades fractional calculus became an area of intense re-search and development.
Kiryakova, Virginia, Machado, Tenreiro, Mainardi, Francesco   +2 more
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Images for the Y‐Function via Marichev–Saigo–Maeda Fractional Integration and Differentiation Operators

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, D. L. Suthar, Shikha Binwal   +2 more
wiley   +1 more source

Mild solutions for a problem involving fractional derivatives in the nonlinearity and in the non-local conditions

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  

LADM procedure to find the analytical solutions of the nonlinear fractional dynamics of partial integro-differential equations

Demonstratio Mathematica
Generally, 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, Khan Hassan, Kumam Poom, Tchier Fairouz, Singh Gurpreet   +4 more
doaj   +1 more source

Trajectory Controllability of Fractional Neutral Stochastic Dynamical Systems of Order α ∈ (1, 2] With Deviating Argument

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, Ravikumar Kasinathan, Ramkumar Kasinathan, Karthikeyan Shanmugasundaram, Dimplekumar Chalishajar, Theodore Simos   +5 more
wiley   +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, Mainardi, Francesco, Tenreiro Machado, J.   +2 more
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Existence and Stability Results for a Modified Diffusion Equation Involving Atangana–Baleanu–Caputo Fractional Derivative

Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.
This article shows another display of the modified diffusion equation of fractional order involving Atangana–Baleanu–Caputo fractional derivative. The manuscript contains three major cases: the existence of a solution, uniqueness of the solution, and Hyers–Ulam stability, which are discussed based on valid theorems in nonlinear analysis.
Maral Sangi, Mohammad Esmael Samei, Arpan Hazra   +2 more
wiley   +1 more source

Fractional nonlocal impulsive quasilinear multi-delay integro-differential systems

Advances in Difference Equations, 2011
In this article, sufficient conditions for the existence result of quasilinear multi-delay integro-differential equations of fractional orders with nonlocal impulsive conditions in Banach spaces have been presented using fractional calculus, resolvent ...
Debbouche Amar
doaj  

Extraction of soliton solutions and Painlevé test for fractional Peyrard-Bishop DNA model

Demonstratio Mathematica
The Peyrard-Bishop DNA model is investigated in this study. Two most reliable and efficient analytical techniques, the Jacobi elliptic function method, and the tanh\tanh -coth\coth method, are being employed for finding new and novel soliton solutions ...
Akram Ghazala, Arshed Saima, Sadaf Maasoomah, De la Sen Manuel, Abbas Muhammad, Hamed Yasser Salah   +5 more
doaj   +1 more source

Solving Fractional Diffusion-Wave Equations Using a New Iterative Method [PDF]

, 2008
Mathematics Subject Classification: 26A33, 31B10In the present paper a New Iterative Method [1] has been employed to find solutions of linear and non-linear fractional diffusion-wave equations.
Bhalekar, Sachin, Daftardar-Gejji, Varsha   +1 more
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