In this paper we study linear and nonlinear fractional diffusion equations with the Caputo
fractional derivative of non-singular kernel that has been launched recently (Caputo and …

Variable-order fractional discrete calculus is a new and unexplored part of calculus that
provides extraordinary capabilities for simulating multidisciplinary processes. Recognizing …

In this paper, we investigate the existence of a unique coupled fixed point for α− admissible
map** which is of F (ψ1, ψ2)− contraction in the context of M− metric space. We have also …

In this article, we derive some novel results of the existence, uniqueness, and stability of the
solution of generalized Caputo-type fractional boundary value problems (FBVPs). The …

In this manuscript, we prove the existence and uniqueness of solutions for local fractional
differential equations (LFDEs) with local fractional derivative operators (LFDOs). By using …

In this paper, we obtain some new results about weakly singular integral inequalities. These
inequalities are used to establish the global existence and uniqueness results for fractional …

A two-point boundary value problem whose highest-order term is a Caputo fractional
derivative of order α∈(1, 2) and where a convection term is also present is considered. Its …

This paper is devoted to studying a class of fractional differential equations (FDEs) with the
Prabhakar fractional derivative of Caputo type in an analytical manner. At first, an estimate of …

In this paper, we study the existence and uniqueness of solutions for fractional differential
equations with fractional integral and Caputo fractional derivatives in boundary conditions …

This paper is concerned with the existence of extremal solutions for periodic boundary value
problems for conformable fractional differential equations with deviating arguments. We first …