In this article, we establish certain sufficient conditions to show the existence of solutions a fractional differential equation with ?-Riemann-Liouville and ?-Caputo derivative in special Banach space. Our approach is based on fixed point theorems for Meir-Keeler condensing operators via measure non-compactness. Also an example given illustrate our approach.

This paper gathers the tools for solving Riemann-Liouville time fractional non-linear PDE’s by using a Galerkin method. method has advantage of not being more complicated than one used to solve same PDE with first order derivative. As model problem, existence and uniqueness is proved semilinear heat equations polynomial growth at infinity.

Recently, a new fractional derivative operator has been introduced so that it presents the combination of Riemann–Liouville integral and Caputo derivative. This paper aims to enhance reproducing kernel Hilbert space method (RKHSM, for short) solving certain differential equations involving this is first time application RKHSM employed some with operator. We illustrate convergence analysis appli...

Our main goal in this paper is to investigate the regularity of mild solution fractional diffusion equation which can be used modelling heat transfer with memory effects. Under some various assumptions input data, we obtain two results. We also provide upper bound and lower source function. The tool use complex evaluations involving Wright

in this paper rationalized haar (rh) functions method is applied to approximate the numerical solution of the fractional volterra integro-differential equations (fvides). the fractional derivatives are described in caputo sense. the properties of rh functions are presented, and the operational matrix of the fractional integration together with the product operational matrix are used to reduce t...

In this article, we study some class of fractional boundary value problem involving generalized Riemann Liouville derivative with respect to a function and the p-Laplace operator. Precisely, using variational methods combined mountain pass theorem, prove that such has nontrivial weak solution. Our main result significantly complement improves previous papers in literature.