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We give a unified interpretation of confluences, contiguity relations and Katz's middle convolutions for linear ordinary differential equations with polynomial coefficients and their generalization to partial differential equations. The…
The existence and stability results for a class of fractional differential equations involving generalized Katugampola derivative are presented herein. Some fixed point theorems are used and enlightening examples of obtained result are also…
This paper is committed to establishing the assumptions essential for the existence and uniqueness results of a fractional functional integrodifferential equation (FFIDE) having a derivative of generalized Hilfer type. Using the Picard…
We prove interior $H^{2s-\varepsilon}$ regularity for weak solutions of linear elliptic integro-differential equations close to the fractional $s$-Laplacian. The result is obtained via intermediate estimates in Nikol'skii spaces, which are…
We study both strict and mild solutions to parabolic evolution equations of the form $dX+AXdt=F(t)dt+G(t)dW(t)$ in Banach spaces. First, we explore the deterministic case. The maximal regularity of solutions has been shown. Second, we…
In this paper we revisit the mild-solution approach to second-order semi-linear PDEs of Hamilton-Jacobi type in infinite-dimensional spaces. We show that a well-known result on existence of mild solutions in Hilbert spaces can be easily…
This article is concerned with the existence and uniqueness of solutions to some fractional order boundary value problems. Our results are based on some fixed point theorems. For the applicability of our results, we provide an example.
The semilinear space-time fractional Schr\"odinger equation is considered. First, we give the explicit form for the fundamental solutions by using the Fox $H$-functions in order to to establish some $L^s$ decay estimates. After that, we…
In this paper, we analyze the existence and uniqueness of generalized weighted pseudo-almost automorphic solutions of abstract Volterra integro-differential inclusions in Banach spaces. The main results are devoted to the study of various…
In this work, we study the initial value problem associated with an abstract integrodifferential equation in interpolation scales. We prove local-in-time existence, uniqueness, continuation, and a blow-up alternative for regular mild…
This paper deals with the existence of asymptotic almost automorphic solution of fractional integro differential equation. We prove the result by using fixed point theorems. We show the result with Lipschitz condition and without Lipschitz…
In this paper, we obtained the sufficient conditions for the existence of solutions to the discrete boundary value problems of fractional difference equation depending on parameters. We use Krasnoselskii fixed point theorem to establish the…
The work considers a system of fractional order partial differential equations. The existence and uniqueness theorems for the classical solution of initial-boundary value problems are proved in two cases: 1) the right-hand side of the…
We obtain some fine gradient estimates near the boundary for solutions to fractional elliptic problems subject to exterior Dirichlet boundary conditions. Our results provide, in particular, the sign of the normal derivative of such…
For a class of non-autonomous parabolic stochastic partial differential equations defined on a bounded open subset $D\subset \mathbb {R}^d$ and driven by an $L^2(D)$-valued fractional Brownian motion with the Hurst index $H>1/2$, a new…
In this paper, we derive the equivalent fractional integral equation to the nonlinear implicit fractional differential equations involving $\varphi$-Hilfer fractional derivative subject to nonlocal fractional integral boundary conditions.…
Recently, a class of efficient spectral Monte-Carlo methods was developed in \cite{Feng2025ExponentiallyAS} for solving fractional Poisson equations. These methods fully consider the low regularity of the solution near boundaries and…
Systems of linear ordinary differential equations with the most general inhomogeneous boundary conditions in fractional Sobolev spaces on a finite interval are studied. The Fredholm property of such problems in corresponding pairs of Banach…
We consider fractional relaxation and fractional oscillation equations involving Erdelyi-Kober integrals. In terms of Riemann-Liouville integrals, the equations we analyze can be understood as equations with time-varying coefficients.…
To study the existence and uniqueness of solutions to Cauchy-type problems for fractional q-difference equations with the bi-ordinal Hilfer fractional q-derivative which is an extension of the Hilfer fractional q-derivative. An approach is…