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In this paper, we study the uniqueness of solutions for a fractional differential equation with dependence on the first order derivative. By means of Banach’s contraction mapping principle and a weighted norm ...
The existence of some class of multi-order nonlinear fractional systems is investigated in this paper. Some sufficient conditions of solutions for multi-order nonlinear systems are obtained based on fixed poin...
In this article, we discuss the sufficient conditions for the existence, uniqueness and stability of solutions to a class of nonlinear impulsive boundary value problem of fractional order differential equation...
Fractional derivatives with three parameter generalized Mittag-Leffler kernels and their properties are studied. The corresponding integral operators are obtained with the help of Laplace transforms. The actio...
A finite difference scheme, based upon the Crank–Nicolson scheme, is applied to the numerical approximation of a two-dimensional time fractional non-Newtonian fluid model. This model not only possesses a multi...
Hadamard fractional derivatives are nonlocal fractional derivatives with singular logarithmic kernel with memory, and hence they are suitable to describe complex systems. In this paper, sufficient conditions a...
In this paper, starting from a fixed δ-sequence, we use the generalized Taylor’s formula based on conformable derivatives and the neutrix limit to find the powers of the Dirac delta function ...
This paper is devoted to the oscillatory problem in the fractional-order delay differential equations. First, we prove the convergence of the Laplace transform of a fractional operator by the generalized Gronw...
In this study, we consider fractional Sturm–Liouville (S–L) problems within non-singular operators. A fractional S–L problem with exponential and Mittag-Leffler kernels is given with different versions in the ...
In this manuscript we investigate the time fractional dispersive long wave equation (DLWE) and its corresponding integer order DLWE. The symmetry properties and reductions are derived. We construct the conserv...