Caputo Fractional Derivatives
The operational matrix of Caputo fractional derivatives of modified generalized Laguerre polynomials and its applications
... of Caputo fractional derivatives is constructed and implemented in combination with the spectral tau method for solving linear multi-term FDEs on the ...of Caputo fractional ...
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Existence and uniqueness of solutions to fractional differential equations in the frame of generalized Caputo fractional derivatives
... generalized Caputo fractional derivative is a name attributed to the Caputo version of the generalized fractional derivative introduced in Jarad et ...to fractional differential ...
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A new operational matrix of Caputo fractional derivatives of Fermat polynomials: an application for solving the Bagley Torvik equation
... Recently, operational matrices have been employed for solving several kinds of differ- ential problems, namely ordinary differential equations, fractional differential equations and integro-differential equations. The ...
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Solution of One –dimensional Fractional Diffusion Equations Involving Caputo Fractional Derivatives in terms of the Mittag Leffler Functions
... In this article, we present the solutions of one-dimensional linear fractional diffusion equations defined by (2.1) and (4.1). The results are derived in a closed form by the application of Laplace and Fourier ...
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2. Hadamard and Fejer-Hadamard inequalities and related results via caputo fractional derivatives
... Actually, fractional calcu- lus is a natural extension of classical ...calculus. Fractional integration and fractional differentiation appear as tools in the subject of partial differential equations ...
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The general solution of differential equations with Caputo Hadamard fractional derivatives and impulsive effect
... Recently, we found the formula of general solution for impulsive systems with Caputo fractional derivatives of order q ∈ (, ) in []. Motivated by the above-mentioned works, we will consider the ...
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5.k-Fractional integral inequalities for harmonically convex functions via Caputo k-fractional derivatives
... Abstract. Fractional integral and differential inequalities provide the bounds for the uniqueness of solutions of the fractional differential ...er-Hadamard fractional inequalities for harmonically ...
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Solving Fractional Derivative of Some Functions
... and Caputo fractional derivatives of algebraic, trigonometric, logarithmic and exponential functions and find they produce same ...and Caputo fractional derivatives differ only ...
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On Caputo modification of the Hadamard fractional derivatives
... tional derivatives could make their study uninteresting and less applicable than Riemann- Liouville and Caputo fractional ...Hadamard derivatives just like the usual derivative D = ...
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On Hadamard and Fej\'{e}r-Hadamard inequalities for Caputo $\small{k}$-fractional derivatives
... fields of science counting rheology, fluid flow, diffusive transport, electrical networks, electromagnetic theory and probability (see [3]). Fourier, Abel, Lacroix, Leibniz, Letnikov and Grunwald contributed a lot in ...
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Fractional order differential systems involving right Caputo and left Riemann–Liouville fractional derivatives with nonlocal coupled conditions
... coupled fractional differential system involving right Caputo and left Riemann–Liouville fractional derivatives, supplemented with nonlocal three-point coupled boundary ...
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SOLUTION OF NON-HOMOGENEOUS DIFFERENTIAL EQUATION WITH THREE AND FOUR FRACTIONAL DERIVATIVES
... nonlinear fractional order differential equations used in the modeling of viscoplasticity, in Scientifice Computing in Chemical Engineering II- Computational Fluid Dynamics, Reaction Engineering and Molecular ...
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On Extended Caputo Fractional Derivative Operator
... extended Caputo fractional derivative operator and establish the extension of an ex- tended fractional derivative of some known elementary ...extended fractional derivative of some familiar ...
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A New Approach for Fractional Order Derivative and Its Applications
... 2) Another important point is that powers of variables decreased as integer during derivation process. There was another assumption in FOD regarded the powers of variables. The coefficients of variables were determined ...
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Incomplete Caputo fractional derivative operators
... of Caputo fractional derivative operators and show their use in the special function ...incomplete Caputo fractional derivative operators and show that the images of some elementary functions ...
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On the solution of two sided fractional ordinary differential equations of Caputo type
... classical fractional derivatives to describe, for ex- ample, relaxation phenomena, processes of oscillation, viscoelastic systems and diffusions in disordered media (anomalous diffusions) among others, have ...
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Variational formulation and optimal control of fractional diffusion equations with Caputo derivatives
... weak Caputo derivative in the sense of distributions (Schwartz []), note that if a distribution function is infinitely differentiable then its Caputo fractional derivative must also ...
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Some New Hermite-Hadamard-Fejer Type Inequlaties via k-Fractional Integrals Concerning Differentiable Generalized Relative Semi-(r; m, h1, h2)-Preinvex Mappings
... type fractional integral inequalities for gener- alized (r; s, m, ϕ)-preinvex functions, ...type fractional integral inequalities for twice differentiable generalized (s, m, ϕ)-preinvex functions, Konuralp ...
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Existence and uniqueness of solution for a boundary value problem of fractional order involving two Caputo’s fractional derivatives
... classical Caputo deriva- tive), where the integrable function h can be discontinuous, is more general than that of the classical Caputo derivative described in (i) in the above lemma (see [] and ...
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Lyapunov type inequalities for nonlinear fractional differential equations and systems involving Caputo type fractional derivatives
... nonlinear fractional differential equations involving Caputo-type fractional derivatives have been ...other fractional boundary value ...
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