Results 161 to 170 of about 2,623 (193)

Fractional Integro-Differential Equations Involving $\psi$-Hilfer Fractional Derivative

Advances in Applied Mathematics and Mechanics, 2019
Summary: Considering a fractional integro-differential equation involving a general form of Hilfer fractional derivative with respect to another function. We show that weighted Cauchy-type problem is equivalent to a Volterra integral equation, we also prove the existence, uniqueness of solutions and Ulam-Hyers stability of this problem by employing a ...
Abdo, Mohammed S., Panchal, Satish K.
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Stochastic differential inclusions with Hilfer fractional derivative

Annals of the University of Craiova, Mathematics and Computer Science Series, 2022
In this paper, we study the existence of mild solutions of Hilfer fractional stochastic differential inclusions driven by sub fractional Brownian motion in the cases when the multivalued map is convex and non convex. The results are obtained by using fixed point theorem. Finally an example is given to illustrate the obtained results.
Meryem Chaouche, Toufik Guendouzi
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Qualitative analysis of fractional differential equations with \(\psi\)-Hilfer fractional derivative

2021
Summary: In this paper, we investigate the solutions of a class of \(\psi\)-Hilfer fractional differential equations with the initial values in the sense of \(\psi\)-fractional integral by using the successive approximation techniques. Next, the continuous dependence of a solution for the given Cauchy-type problem is presented.
Baghani, Omid, Harikrishnan, S, Kanagarajan, K   +2 more
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On the $��$-Hilfer fractional derivative

2017
In this paper we introduce a new fractional derivative with respect to another function the so-called $ $-Hilfer fractional derivative. We discuss some properties and important results of the fractional calculus. In this sense, we present some uniformly convergent sequence of function results and examples involving the Mittag-Leffler function with one
Sousa, J. Vanterler da C., de Oliveira, E. Capelas   +1 more
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Leibniz type rule: $��-$Hilfer fractional derivative

2018
In this paper, we present the Leibniz rule for the $ -$Hilfer ($ -$H) fractional derivative in two versions, the first in relation to $ -$RL fractional derivative and the second in relation to the $ -$H fractional derivative. In this sense, we present some particular cases of Leibniz rules and Leibniz type rules from the investigated case.
Sousa, J. Vanterler da C., de Oliveira, E. Capelas   +1 more
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Controllability of fractional dynamical systems with $$(k,\psi )$$-Hilfer fractional derivative

Journal of Applied Mathematics and Computing
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Haque, Inzamamul, Ali, Javid, Malik, Muslim   +2 more
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Existence theory of fractional coupled differential equations via Ψ-Hilfer fractional derivative

Random Operators and Stochastic Equations, 2019
Abstract In this paper, we analyze existence results for coupled differential equations via ψ- Hilfer fractional derivative. The proof relies on the Schaefer fixed point theorem.
Sugumaran Harikrishnan, Kamal Shah, Kuppusamy Kanagarajan   +2 more
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A Study on Langevin Equations with ψ-Hilfer Fractional Derivative

The interdisciplinary journal of Discontinuity, Nonlinearity, and Complexity, 2019
Summary: In this paper, we discuss the existence, uniqueness and four types of Ulam stability results for a general class of Langevin equations. An example is given to illustrate the applicability of these results.
Harikrishnan, S., Kanagarajan, K., Vivek, D.   +2 more
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Lagrangians With Linear Velocities Within Hilfer Fractional Derivative

Volume 3: 2011 ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications, Parts A and B, 2011
Fractional variational principles started to be one of the major area in the field of fractional calculus. During the last few years the fractional variational principles were developed within several fractional derivatives. One of them is the Hilfer’s generalized fractional derivative which interpolates between Riemann-Liouville and Caputo fractional ...
Dumitru Baleanu, Om P. Agrawal, Sami I. Muslih   +2 more
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Existence results for hybrid fractional differential equations with Hilfer fractional derivative

2020
Summary: This paper investigates the solvability, existence and uniqueness of solutions for a class of nonlinear fractional hybrid differential equations with Hilfer fractional derivative in a weighted normed space. The main result is proved by means of a fixed point theorem due to Dhage. An example to illustrate the results is included.
Baghani, O., Vivek, D., Kanagarajan, k
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