On the local fractional wave equation in fractal strings

Abstract

The key aim of the present study is to attain nondifferentiable solutions of extended wave equation by making use of a local fractional derivative describing fractal strings by applying local fractional homotopy perturbation Laplace transform scheme. The convergence and uniqueness of the obtained solution by using suggested scheme is also examined. To determine the computational efficiency of offered scheme, some numerical examples are discussed. The results extracted with the aid of this technique verify that the suggested algorithm is suitable to execute, and numerical computational work is very interesting.

Positive solution of nonlinear fractional differential equations with Caputo‐like counterpart hyper‐Bessel operators

“…Hence, Theorem 2.10 yields that F has a fixed point in U. Namely, it is a solution of Equation (11). Since the arbitrariness of T ∈ (0, +∞), then we claim that there exists a positive solution u ∈ C[0, +∞) of Equation (11).…”

“…Theorem 4.1. Set f(t) ∈ C[0, +∞); then, there exists a explicit solution of problem (11), which is given in the integral form…”

“…Fractional differential equations are becoming more and more adequate than those of integer order in studying related problems in various fields, such as engineering, physics, and economics, because fractional derivatives describe the property of memory and heredity of many materials.…”

Coupled System of Nonlinear Fractional Langevin Equations with Multipoint and Nonlocal Integral Boundary Conditions

“…Fractional calculus was an essential element in many recently published articles, such as a fractional biological population model, a fractional SISR-SI malaria disease model, a fractional Biswas-Milovic model, fractional wave equations, fractional reaction-diffusion equations, and nonlinear fractional shock wave equations. More recent published articles related with fractional calculus can be clearly found in [1][2][3][4][5][6][7][8][9]. Fractional differential equations have obtained a remarkable reputation among the mathematicians due to rapid development which is applicable in many fields such as mathematics, chemistry, and electronics.…”

A fractional sideways problem in a one‐dimensional finite‐slab with deterministic and random interior perturbed data

“…conduction problem arises from many branches of engineering sciences. 6,7 Then the fractional calculus has encountered much success in many fields of science: mathematics, physics, [3][4][5][8][9][10] chemistry, 11 biological systems 12 and so on. 2,13,14 In the present paper, we will consider the fractional diffusion equation D t u(x, t) = u xx (x, t), (x, t) ∈ Ω.…”