In this paper, we derive the representation formula of solution for ?-Hilfer fractional differential equation with constant coefficient in form Mittag-Leffler function by using Picard’s successive approximation. Moreover, some properties and fixed point theorems such as Banach Schaefer, introduce new results qualitative existence uniqueness. The generalized Gronwall inequality lemma is used ana...

In the framework of Hilbert spaces we shall give necessary and sufficient conditions to define a Dirichlet-to-Neumann operator via Dirichlet principle. Analyzing singular operators, will establish Laurent expansion near singularities as well Mittag–Leffler for related quadratic forms. The established results be exploited solve definitively problem positivity semigroup in Lebesgue spaces. obtain...

In this paper, we investigate two inverse source problems for degenerate time-fractional partial differential equation in rectangular domains. The first problem involves a space-degenerate and the second one time-degenerate equation. Solutions to both are expressed series expansions. For problem, obtained solutions form of Fourier-Legendre series. Convergence uniqueness have been discussed. Fou...

Transient heat conduction problems are systematically applied to the fading memory formalism with different Mittag-Leffler-type kernels. With such an approach, using various memories naturally results in definitions of fractional operators. Six examples given and interpreted from a common perspective, covering most well-liked versions Mittag-Leffler function. The approach was used as template d...

Abstract In this article, first, we present an example of fuzzy normed space by means the Mittag-Leffler function. Next, extend concept to matrix valued and also introduce a class control functions stabilize nonlinear ϕ -Hadamard fractional Volterra integro-differential equation. sense, investigate Ulam–Hyers–Rassias stability for kind equations in Banach space. Finally, as application, using f...

We introduce the Segal-Bargmann transform associated to Mittag Leffler Fock space and study how it will be connected Fourier transform.We discuss also counterpart of creation annihilation operator in this setting using Caputo Liouville operators. Finally, we give an extension these results case quaternions, particular slice hyperholomorphic setting.