In this paper, we concern with an exponential nonlinearity for a fractional wave equation in
the whole space, we establish the local existence of solutions in a dense subspace of the …

In this paper, we first establish a modified Marcinkiewicz interpolation result, and using this
result, we obtain a new regularity result for a fractional Laplacian problem on a bounded C …

The initial value problem for the Caputo type time‐fractional Sobolev equation with a
nonlinear exponential source function is investigated in this work. We establish the …

The fractional calculus started more than three centuries ago. In the last years, the fractional
calculus is playing a very important role in various scientific fields. In fact, it has been …

In this paper, we study a Cauchy problem for a space–time fractional diffusion equation with
exponential nonlinearity. Based on the standard Lp-Lq estimates of strongly continuous …

We investigate the Cauchy problem for a heat equation involving a fractional harmonic
oscillator and an exponential nonlinearity. Our main contributions are as follows:-We …

We consider the initial-boundary value problem for the heat equation in the half space with
an exponential nonlinear boundary condition. We prove the existence of global-in-time …

Nonexistence for fractional differential inequalities and systems in the sense of Erd\'elyi-Kober
Page 1 https://www.aimspress.com/journal/Math AIMS Mathematics, 9(8): 21686–21702 …

In the paper, we focus on the local existence and blow-up of solutions for a time fractional
nonlinear equation with biharmonic operator and exponentional nonlinear memory in an …

In this chapter, we first study the well-posedness and regularity of mild solutions for a class
of time fractional damped wave equations. A concept of mild solutions is introduced to prove …