A new time-fractional derivative with Mittag-Leffler memory kernel, called the generalized Atangana-Baleanu is defined along associated integral operator. Some properties of operators are proved. The operator suitable to generate by particularization known Atangana-Baleanu, Caputo-Fabrizio and Caputo derivatives. mathematical model advection-dispersion process kinetic adsorption formulated cons...

We present uniform and $L_p$ mixed Caputo-Bochner abstract generalized fractional Landau inequalities over $\mathbb{R}$ of orders $2 < \alpha \leq 3 $. These estimate the size first second derivatives a composition with Banach space valued function $\mathbb{R}$. give applications when $? = 2.5$.

In this study, we establish a novel version of Hermite-Hadamard inequalities through neoteric generalized Riemann-Liouville fractional integrals (RLFIs). For functions with the convex absolute values derivatives, create variety midpoint and trapezoid form inequalities, including RLFIs. Moreover, multiple can be produced as special cases findings study.

This paper deals with the investigation of the computational solutions of a unified fractional reaction-diffusion equation, which is obtained from the standard diffusion equation by replacing the time derivative of first order by the generalized Riemann–Liouville fractional derivative defined by others and the space derivative of second order by the Riesz–Feller fractional derivative and adding...

Fractional calculus was formulated in 1695, shortly after the development of classical calculus. The earliest systematic studies were attributed to Liouville, Riemann, Leibniz, etc. [1,2]. For a long time, fractional calculus has been regarded as a pure mathematical realm without real applications. But, in recent decades, such a state of affairs has been changed. It has been found that fraction...

Fractional order derivative operators offer a concise description to model multi-scale, heterogeneous and non-local systems. Specifically, in magnetic resonance imaging, there has been recent work to apply fractional order derivatives to model the non-Gaussian diffusion signal, which is ubiquitous in the movement of water protons within biological tissue. To provide a new perspective for establ...

In this paper, we consider spectral approximation of fractional differential equations (FDEs). A main ingredient of our approach is to define a new class of generalized Jacobi functions (GJFs), which is intrinsically related to fractional calculus and can serve as natural basis functions for properly designed spectral methods for FDEs. We establish spectral approximation results for these GJFs ...

This paper establishes some closed formulas for RiemannLiouville impulsive fractional integral calculus and also for RiemannLiouville and Caputo impulsive fractional derivatives. Keywords—RimannLiouville fractional calculus, Caputo fractional derivative, Dirac delta, Distributional derivatives, Highorder distributional derivatives.