In this paper, we aim to propose a novel analytical method for obtaining atomic solutions to
partial differential equations. A theory of tensor products in Banach spaces is utilized and …

In this paper, we establish sufficient conditions for the existence and uniqueness of solution
for a class of initial boundary value problems with Dirichlet condition in regard to a category …

Several real-world phenomena emerging in engineering and science fields can be
described successfully by develo** certain models using fractional-order partial …

The use of classical methods to solve some fractional partial differential equations, usually,
leads to dead ends with no possible solutions as the separation of variables. Hence, in this …

In this paper, we establish sufficient conditions for the existence and uniqueness of the
solution for a class of initial-boundary value problems with Dirichlet condition for a class of …

In this paper, a new collocation method based on the Pell–Lucas polynomials is presented
to solve the parabolic-type partial Volterra integro-differential equations. According to the …

In this paper, two problems involving nonlinear time fractional hyperbolic partial differential
equations (PDEs) and time fractional pseudo hyperbolic PDEs with nonlocal conditions are …

Solvability of the Solution of Superlinear Hyperbolic Dirichlet Problem Page 1 Int. J. Anal.
Appl. (2022), 20:62 Solvability of the Solution of Superlinear Hyperbolic Dirichlet Problem …

In this paper, we present and discuss a class of semi-linear heat equation with nonlinear
nonlocal conditions of second type. The existence and uniqueness of weak solution of the …

In this work, we aim to propose a mathematical formalism for the human liver involving
Caputo fractional derivative (CFD) with modified parameters. Regarding the proposed …