Results 81 to 90 of about 372,508 (154)
Analytic solutions of fractional differential equations by operational methods
, 2012 We describe a general operational method that can be used in the analysis of fractional initial and boundary value problems with additional analytic conditions. As an example, we derive analytic solutions of some fractional generalisation of differential
Garra, Roberto, Polito, Federico
core +1 more source
Journal of the Nigerian Society of Physical Sciences, 2023 Visceral leishmaniosis is one recent example of a global illness that demands our best efforts at understanding. Thus, mathematical modeling may be utilized to learn more about and make better epidemic forecasts. By taking into account the Caputo and Caputo-Fabrizio derivatives, a frictional model of visceral leishmaniosis was mathematically examined ...
Dalal Khalid Almutairi +5 more
openaire +2 more sources
Mathematical Methods in the Applied Sciences, EarlyView.A highly accurate numerical method is given for the solution of boundary value problem of generalized Bagley‐Torvik (BgT) equation with Caputo derivative of order 0<β<2$$ 0<\beta <2 $$ by using the collocation‐shooting method (C‐SM). The collocation solution is constructed in the space Sm+1(1)$$ {S}_{m+1}^{(1)} $$ as piecewise polynomials of degree at ...
Suzan Cival Buranay +2 more
wiley +1 more source
A PRIORI ESTIMATION OF A GENERALIZED NONLOCAL BOUNDARY VALUE PROBLEM FOR A THRID ORDER EQUATION WITH A FRACTIONAL TIME CAPUTO DERIVATIVE [PDF]
Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2019 A boundary value problem for a third-order parabolic equation with a fractional Caputo derivative is considered. A priori estimation of the solution of a generalized nonlocal boundary value problem for an equation with multiple characteristics with a ...
A. M. Shkhagapsoev
doaj +1 more source
Fractional Euler-Lagrange differential equations via Caputo derivatives [PDF]
Fractional Dynamics and Control, Springer New York, 2012, 109-118, 2011 We review some recent results of the fractional variational calculus. Necessary optimality conditions of Euler-Lagrange type for functionals with a Lagrangian containing left and right Caputo derivatives are given. Several problems are considered: with fixed or free boundary conditions, and in presence of integral constraints that also depend on Caputo
arxiv +1 more source
Blowing‐Up Solution of a System of Fractional Differential Equations With Variable Order
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT We investigated the necessary condition for blowing‐up solutions in finite time of the system u′(t)+(1)D0|tα(t)(u(t)−u0)=|v(t)|q,t>0,q>1,v′(t)+(1)D0|tβ(t)(v(t)−v0)=|u(t)|p,t>0,p>1$$ {u}^{\prime }(t)+{}_{(1)}{D}_{0\mid t}^{\alpha (t)}\left(u(t)-{u}_0\right)={\left|v(t)\right|}^q,\kern0.3em t>0,q>1,{v}^{\prime }(t)+{}_{(1)}{D}_{0\mid t}^{\beta ...
Muhammad Rizki Fadillah, Mokhtar Kirane
wiley +1 more source
Fractional Mass-Spring-Damper System Described by Generalized Fractional Order Derivatives
Fractal and Fractional, 2019 This paper proposes novel analytical solutions of the mass-spring-damper systems described by certain generalized fractional derivatives. The Liouville−Caputo left generalized fractional derivative and the left generalized fractional derivative ...
Ndolane Sene +1 more
doaj +1 more source
Necessary conditions to a fractional variational problem [PDF]
arXiv, 2021 In order to solve fractional variational problems, there exist two theorems of necessary conditions: an Euler-Lagrange equation which involves Caputo and Riemann-Liouville fractional derivatives, and other Euler-Lagrange equation that involves only Caputo derivatives.
arxiv
Infrared spectroscopy of diatomic molecules - a fractional calculus approach
, 2012 The eigenvalue spectrum of the fractional quantum harmonic oscillator is calculated numerically solving the fractional Schr\"odinger equation based on the Riemann and Caputo definition of a fractional derivative.
Dirac P. A. M. +20 more
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Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT In this article, we provided fixed‐point results for (Θ,G1)$$ \left(\Theta, {G}_1\right) $$‐quasirational contraction and (Θ,G2)$$ \left(\Theta, {G}_2\right) $$‐quasirational contraction within the setting of triple controlled metric‐like spaces.
Sadia Farooq +3 more
wiley +1 more source